bring one expression to another one

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I'm trying to bring this expression:

$$frac56logleft(frac54right) - frac16log(2)$$

To this one:

$$logleft(frac54right) - frac16logleft(frac52right)$$

Where $log$ is the natural algorithm.

I know the two expressions are equal (checked with wolfram) but I really can't find the correct passages... Could you please help me?

algebra-precalculus logarithms

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edited 2 hours ago

Rory Daulton

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asked 2 hours ago

Alessio Martorana

957

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up vote
1
down vote

favorite

I'm trying to bring this expression:

$$frac56logleft(frac54right) - frac16log(2)$$

To this one:

$$logleft(frac54right) - frac16logleft(frac52right)$$

Where $log$ is the natural algorithm.

I know the two expressions are equal (checked with wolfram) but I really can't find the correct passages... Could you please help me?

algebra-precalculus logarithms

share|cite|improve this question

edited 2 hours ago

Rory Daulton

29.1k53253

asked 2 hours ago

Alessio Martorana

957

add a comment | 

up vote
1
down vote

favorite

up vote
1
down vote

favorite

I'm trying to bring this expression:

$$frac56logleft(frac54right) - frac16log(2)$$

To this one:

$$logleft(frac54right) - frac16logleft(frac52right)$$

Where $log$ is the natural algorithm.

I know the two expressions are equal (checked with wolfram) but I really can't find the correct passages... Could you please help me?

algebra-precalculus logarithms

share|cite|improve this question

edited 2 hours ago

Rory Daulton

29.1k53253

asked 2 hours ago

Alessio Martorana

957

I'm trying to bring this expression:

$$frac56logleft(frac54right) - frac16log(2)$$

To this one:

$$logleft(frac54right) - frac16logleft(frac52right)$$

Where $log$ is the natural algorithm.

I know the two expressions are equal (checked with wolfram) but I really can't find the correct passages... Could you please help me?

algebra-precalculus logarithms

algebra-precalculus logarithms

share|cite|improve this question

edited 2 hours ago

Rory Daulton

29.1k53253

asked 2 hours ago

Alessio Martorana

957

share|cite|improve this question

edited 2 hours ago

Rory Daulton

29.1k53253

asked 2 hours ago

Alessio Martorana

957

share|cite|improve this question

share|cite|improve this question

edited 2 hours ago

Rory Daulton

29.1k53253

edited 2 hours ago

Rory Daulton

29.1k53253

edited 2 hours ago

Rory Daulton

29.1k53253

29.1k53253

asked 2 hours ago

Alessio Martorana

957

asked 2 hours ago

Alessio Martorana

957

asked 2 hours ago

Alessio Martorana

957

957

add a comment | 

add a comment | 

5 Answers
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up vote
1
down vote



accepted

$frac56logleft(frac54right)-frac16log(2)=logleft(frac54right)-frac16logleft(frac54right)-frac16log(2)$

$= logleft(frac54right)-(frac16logleft(frac54right)+frac16log(2))$

$=logleft(frac54right)-frac16logleft(frac5cdot24right)$

$=logleft(frac54right)-frac16logleft(frac52right)$

I should add: Subtracting logs is equivalent to division. The reason for potential problems here is $fracfracabc = fracabcdot c$ and not $fraca(fracbc)$

share|cite|improve this answer

edited 37 mins ago

answered 2 hours ago

Phil H

2,2982311

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up vote
3
down vote

Hint: Begin with$$frac56logleft(frac54right)-frac16log(2)=logleft(frac54right)-frac16logleft(frac54right)-frac16log(2).$$

share|cite|improve this answer

answered 2 hours ago

José Carlos Santos

123k17101186

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Ty very much for the hint, I was on the right road, but missed the last passage that, imho, Phil stated very simply and clear
  – Alessio Martorana
  1 hour ago
  

  
  
  
  

add a comment | 

up vote
1
down vote

We have

$$frac56logleft(frac54right) - frac16log 2=overbracefrac56logleft(frac54right)+colorredfrac16logleft(frac54right) -overbracecolorredfrac16logleft(frac54right)- frac16log 2=$$

$$=logleft(frac54right)-frac16 logleft(frac52right)$$

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answered 2 hours ago

gimusi

74.1k73889

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$$fraccolorblue56log frac54 - frac16log 2 = fraccolorblue6-16logfrac54 - frac16log2 = log frac54 - frac16left(colorgreenlogfrac54 + log 2 right)$$$$ = log frac54 - frac16colorgreen log left( frac54 cdot 2 right) = log frac54 - frac16 log frac52 $$

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answered 2 hours ago

trancelocation

5,8781516

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Alt. hint:   by brute force, using only $,log fracab = log a - log b,$ and $,log a^n = n log a,$:

$$small
frac56logfrac54 - frac16log 2 = frac16left(5 log 5 - 5 log 4-log 2right) = frac16left(5 log 5 - 10 log 2-log 2right) = frac16left(5 log 5 - 11 log 2right)
$$

Now do the same for $,log frac54 - frac16log frac52,$ and compare.

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answered 2 hours ago

dxiv

56.3k64798

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5 Answers
5

active

oldest

votes

5 Answers
5

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote



accepted

$frac56logleft(frac54right)-frac16log(2)=logleft(frac54right)-frac16logleft(frac54right)-frac16log(2)$

$= logleft(frac54right)-(frac16logleft(frac54right)+frac16log(2))$

$=logleft(frac54right)-frac16logleft(frac5cdot24right)$

$=logleft(frac54right)-frac16logleft(frac52right)$

I should add: Subtracting logs is equivalent to division. The reason for potential problems here is $fracfracabc = fracabcdot c$ and not $fraca(fracbc)$

share|cite|improve this answer

edited 37 mins ago

answered 2 hours ago

Phil H

2,2982311

add a comment | 

up vote
1
down vote



accepted

$frac56logleft(frac54right)-frac16log(2)=logleft(frac54right)-frac16logleft(frac54right)-frac16log(2)$

$= logleft(frac54right)-(frac16logleft(frac54right)+frac16log(2))$

$=logleft(frac54right)-frac16logleft(frac5cdot24right)$

$=logleft(frac54right)-frac16logleft(frac52right)$

I should add: Subtracting logs is equivalent to division. The reason for potential problems here is $fracfracabc = fracabcdot c$ and not $fraca(fracbc)$

share|cite|improve this answer

edited 37 mins ago

answered 2 hours ago

Phil H

2,2982311

add a comment | 

up vote
1
down vote



accepted

up vote
1
down vote



accepted

$frac56logleft(frac54right)-frac16log(2)=logleft(frac54right)-frac16logleft(frac54right)-frac16log(2)$

$= logleft(frac54right)-(frac16logleft(frac54right)+frac16log(2))$

$=logleft(frac54right)-frac16logleft(frac5cdot24right)$

$=logleft(frac54right)-frac16logleft(frac52right)$

I should add: Subtracting logs is equivalent to division. The reason for potential problems here is $fracfracabc = fracabcdot c$ and not $fraca(fracbc)$

share|cite|improve this answer

edited 37 mins ago

answered 2 hours ago

Phil H

2,2982311

$frac56logleft(frac54right)-frac16log(2)=logleft(frac54right)-frac16logleft(frac54right)-frac16log(2)$

$= logleft(frac54right)-(frac16logleft(frac54right)+frac16log(2))$

$=logleft(frac54right)-frac16logleft(frac5cdot24right)$

$=logleft(frac54right)-frac16logleft(frac52right)$

I should add: Subtracting logs is equivalent to division. The reason for potential problems here is $fracfracabc = fracabcdot c$ and not $fraca(fracbc)$

share|cite|improve this answer

edited 37 mins ago

answered 2 hours ago

Phil H

2,2982311

share|cite|improve this answer

share|cite|improve this answer

edited 37 mins ago

edited 37 mins ago

edited 37 mins ago

answered 2 hours ago

Phil H

2,2982311

answered 2 hours ago

Phil H

2,2982311

answered 2 hours ago

Phil H

2,2982311

2,2982311

add a comment | 

add a comment | 

up vote
3
down vote

Hint: Begin with$$frac56logleft(frac54right)-frac16log(2)=logleft(frac54right)-frac16logleft(frac54right)-frac16log(2).$$

share|cite|improve this answer

answered 2 hours ago

José Carlos Santos

123k17101186

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Ty very much for the hint, I was on the right road, but missed the last passage that, imho, Phil stated very simply and clear
  – Alessio Martorana
  1 hour ago
  

  
  
  
  

add a comment | 

up vote
3
down vote

Hint: Begin with$$frac56logleft(frac54right)-frac16log(2)=logleft(frac54right)-frac16logleft(frac54right)-frac16log(2).$$

share|cite|improve this answer

answered 2 hours ago

José Carlos Santos

123k17101186

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Ty very much for the hint, I was on the right road, but missed the last passage that, imho, Phil stated very simply and clear
  – Alessio Martorana
  1 hour ago
  

  
  
  
  

add a comment | 

up vote
3
down vote

up vote
3
down vote

Hint: Begin with$$frac56logleft(frac54right)-frac16log(2)=logleft(frac54right)-frac16logleft(frac54right)-frac16log(2).$$

share|cite|improve this answer

answered 2 hours ago

José Carlos Santos

123k17101186

Hint: Begin with$$frac56logleft(frac54right)-frac16log(2)=logleft(frac54right)-frac16logleft(frac54right)-frac16log(2).$$

share|cite|improve this answer

answered 2 hours ago

José Carlos Santos

123k17101186

share|cite|improve this answer

share|cite|improve this answer

answered 2 hours ago

José Carlos Santos

123k17101186

answered 2 hours ago

José Carlos Santos

123k17101186

answered 2 hours ago

José Carlos Santos

123k17101186

123k17101186

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Ty very much for the hint, I was on the right road, but missed the last passage that, imho, Phil stated very simply and clear
  – Alessio Martorana
  1 hour ago
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Ty very much for the hint, I was on the right road, but missed the last passage that, imho, Phil stated very simply and clear
  – Alessio Martorana
  1 hour ago
  

  
  
  
  

Ty very much for the hint, I was on the right road, but missed the last passage that, imho, Phil stated very simply and clear
– Alessio Martorana
1 hour ago

Ty very much for the hint, I was on the right road, but missed the last passage that, imho, Phil stated very simply and clear
– Alessio Martorana
1 hour ago

add a comment | 

up vote
1
down vote

We have

$$frac56logleft(frac54right) - frac16log 2=overbracefrac56logleft(frac54right)+colorredfrac16logleft(frac54right) -overbracecolorredfrac16logleft(frac54right)- frac16log 2=$$

$$=logleft(frac54right)-frac16 logleft(frac52right)$$

share|cite|improve this answer

answered 2 hours ago

gimusi

74.1k73889

add a comment | 

up vote
1
down vote

We have

$$frac56logleft(frac54right) - frac16log 2=overbracefrac56logleft(frac54right)+colorredfrac16logleft(frac54right) -overbracecolorredfrac16logleft(frac54right)- frac16log 2=$$

$$=logleft(frac54right)-frac16 logleft(frac52right)$$

share|cite|improve this answer

answered 2 hours ago

gimusi

74.1k73889

add a comment | 

up vote
1
down vote

up vote
1
down vote

We have

$$frac56logleft(frac54right) - frac16log 2=overbracefrac56logleft(frac54right)+colorredfrac16logleft(frac54right) -overbracecolorredfrac16logleft(frac54right)- frac16log 2=$$

$$=logleft(frac54right)-frac16 logleft(frac52right)$$

share|cite|improve this answer

answered 2 hours ago

gimusi

74.1k73889

We have

$$frac56logleft(frac54right) - frac16log 2=overbracefrac56logleft(frac54right)+colorredfrac16logleft(frac54right) -overbracecolorredfrac16logleft(frac54right)- frac16log 2=$$

$$=logleft(frac54right)-frac16 logleft(frac52right)$$

share|cite|improve this answer

answered 2 hours ago

gimusi

74.1k73889

share|cite|improve this answer

share|cite|improve this answer

answered 2 hours ago

gimusi

74.1k73889

answered 2 hours ago

gimusi

74.1k73889

answered 2 hours ago

gimusi

74.1k73889

74.1k73889

add a comment | 

add a comment | 

up vote
0
down vote

$$fraccolorblue56log frac54 - frac16log 2 = fraccolorblue6-16logfrac54 - frac16log2 = log frac54 - frac16left(colorgreenlogfrac54 + log 2 right)$$$$ = log frac54 - frac16colorgreen log left( frac54 cdot 2 right) = log frac54 - frac16 log frac52 $$

share|cite|improve this answer

answered 2 hours ago

trancelocation

5,8781516

add a comment | 

up vote
0
down vote

$$fraccolorblue56log frac54 - frac16log 2 = fraccolorblue6-16logfrac54 - frac16log2 = log frac54 - frac16left(colorgreenlogfrac54 + log 2 right)$$$$ = log frac54 - frac16colorgreen log left( frac54 cdot 2 right) = log frac54 - frac16 log frac52 $$

share|cite|improve this answer

answered 2 hours ago

trancelocation

5,8781516

add a comment | 

up vote
0
down vote

up vote
0
down vote

$$fraccolorblue56log frac54 - frac16log 2 = fraccolorblue6-16logfrac54 - frac16log2 = log frac54 - frac16left(colorgreenlogfrac54 + log 2 right)$$$$ = log frac54 - frac16colorgreen log left( frac54 cdot 2 right) = log frac54 - frac16 log frac52 $$

share|cite|improve this answer

answered 2 hours ago

trancelocation

5,8781516

$$fraccolorblue56log frac54 - frac16log 2 = fraccolorblue6-16logfrac54 - frac16log2 = log frac54 - frac16left(colorgreenlogfrac54 + log 2 right)$$$$ = log frac54 - frac16colorgreen log left( frac54 cdot 2 right) = log frac54 - frac16 log frac52 $$

share|cite|improve this answer

answered 2 hours ago

trancelocation

5,8781516

share|cite|improve this answer

share|cite|improve this answer

answered 2 hours ago

trancelocation

5,8781516

answered 2 hours ago

trancelocation

5,8781516

answered 2 hours ago

trancelocation

5,8781516

5,8781516

add a comment | 

add a comment | 

up vote
0
down vote

Alt. hint:   by brute force, using only $,log fracab = log a - log b,$ and $,log a^n = n log a,$:

$$small
frac56logfrac54 - frac16log 2 = frac16left(5 log 5 - 5 log 4-log 2right) = frac16left(5 log 5 - 10 log 2-log 2right) = frac16left(5 log 5 - 11 log 2right)
$$

Now do the same for $,log frac54 - frac16log frac52,$ and compare.

share|cite|improve this answer

answered 2 hours ago

dxiv

56.3k64798

add a comment | 

up vote
0
down vote

Alt. hint:   by brute force, using only $,log fracab = log a - log b,$ and $,log a^n = n log a,$:

$$small
frac56logfrac54 - frac16log 2 = frac16left(5 log 5 - 5 log 4-log 2right) = frac16left(5 log 5 - 10 log 2-log 2right) = frac16left(5 log 5 - 11 log 2right)
$$

Now do the same for $,log frac54 - frac16log frac52,$ and compare.

share|cite|improve this answer

answered 2 hours ago

dxiv

56.3k64798

add a comment | 

up vote
0
down vote

up vote
0
down vote

Alt. hint:   by brute force, using only $,log fracab = log a - log b,$ and $,log a^n = n log a,$:

$$small
frac56logfrac54 - frac16log 2 = frac16left(5 log 5 - 5 log 4-log 2right) = frac16left(5 log 5 - 10 log 2-log 2right) = frac16left(5 log 5 - 11 log 2right)
$$

Now do the same for $,log frac54 - frac16log frac52,$ and compare.

share|cite|improve this answer

answered 2 hours ago

dxiv

56.3k64798

Alt. hint:   by brute force, using only $,log fracab = log a - log b,$ and $,log a^n = n log a,$:

$$small
frac56logfrac54 - frac16log 2 = frac16left(5 log 5 - 5 log 4-log 2right) = frac16left(5 log 5 - 10 log 2-log 2right) = frac16left(5 log 5 - 11 log 2right)
$$

Now do the same for $,log frac54 - frac16log frac52,$ and compare.

share|cite|improve this answer

answered 2 hours ago

dxiv

56.3k64798

share|cite|improve this answer

share|cite|improve this answer

answered 2 hours ago

dxiv

56.3k64798

answered 2 hours ago

dxiv

56.3k64798

answered 2 hours ago

dxiv

56.3k64798

56.3k64798

add a comment | 

add a comment | 

 

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