How to solve $log_frac13(frac3x-1x+2)>0$. [closed]

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How to solve

$$log_frac13(dfrac3x-1x+2)>0$$

I am not sure how to solve it.

algebra-precalculus inequality

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edited Jul 28 at 17:06

user 108128

19k41544

asked Jul 28 at 16:54

UltimateMath

385

closed as off-topic by amWhy, Claude Leibovici, Taroccoesbrocco, Xander Henderson, user223391 Jul 30 at 0:04

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Claude Leibovici, Taroccoesbrocco, Xander Henderson, Community

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Hint $log(fracab) = log(a) - log(b)$
  – Good Morning Captain
  Jul 28 at 16:56
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @GoodMorningCaptain this only if numerator and denominator are both positive.
  – Vera
  Jul 28 at 16:57
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

How to solve

$$log_frac13(dfrac3x-1x+2)>0$$

I am not sure how to solve it.

algebra-precalculus inequality

share|cite|improve this question

edited Jul 28 at 17:06

user 108128

19k41544

asked Jul 28 at 16:54

UltimateMath

385

closed as off-topic by amWhy, Claude Leibovici, Taroccoesbrocco, Xander Henderson, user223391 Jul 30 at 0:04

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Claude Leibovici, Taroccoesbrocco, Xander Henderson, Community

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Hint $log(fracab) = log(a) - log(b)$
  – Good Morning Captain
  Jul 28 at 16:56
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @GoodMorningCaptain this only if numerator and denominator are both positive.
  – Vera
  Jul 28 at 16:57
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

up vote
0
down vote

favorite

How to solve

$$log_frac13(dfrac3x-1x+2)>0$$

I am not sure how to solve it.

algebra-precalculus inequality

share|cite|improve this question

edited Jul 28 at 17:06

user 108128

19k41544

asked Jul 28 at 16:54

UltimateMath

385

How to solve

$$log_frac13(dfrac3x-1x+2)>0$$

I am not sure how to solve it.

algebra-precalculus inequality

share|cite|improve this question

edited Jul 28 at 17:06

user 108128

19k41544

asked Jul 28 at 16:54

UltimateMath

385

share|cite|improve this question

share|cite|improve this question

edited Jul 28 at 17:06

user 108128

19k41544

edited Jul 28 at 17:06

user 108128

19k41544

edited Jul 28 at 17:06

user 108128

19k41544

19k41544

asked Jul 28 at 16:54

UltimateMath

385

asked Jul 28 at 16:54

UltimateMath

385

asked Jul 28 at 16:54

UltimateMath

385

385

closed as off-topic by amWhy, Claude Leibovici, Taroccoesbrocco, Xander Henderson, user223391 Jul 30 at 0:04

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Claude Leibovici, Taroccoesbrocco, Xander Henderson, Community

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by amWhy, Claude Leibovici, Taroccoesbrocco, Xander Henderson, user223391 Jul 30 at 0:04

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Claude Leibovici, Taroccoesbrocco, Xander Henderson, Community

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Hint $log(fracab) = log(a) - log(b)$
  – Good Morning Captain
  Jul 28 at 16:56
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @GoodMorningCaptain this only if numerator and denominator are both positive.
  – Vera
  Jul 28 at 16:57
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Hint $log(fracab) = log(a) - log(b)$
  – Good Morning Captain
  Jul 28 at 16:56
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @GoodMorningCaptain this only if numerator and denominator are both positive.
  – Vera
  Jul 28 at 16:57
  

  
  
  
  

Hint $log(fracab) = log(a) - log(b)$
– Good Morning Captain
Jul 28 at 16:56

Hint $log(fracab) = log(a) - log(b)$
– Good Morning Captain
Jul 28 at 16:56

@GoodMorningCaptain this only if numerator and denominator are both positive.
– Vera
Jul 28 at 16:57

@GoodMorningCaptain this only if numerator and denominator are both positive.
– Vera
Jul 28 at 16:57

add a comment | 

2 Answers
2

active

oldest

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up vote
2
down vote



accepted

Hint:
$$log_(1/3)left(frac3x-1x+2right)=-log_3left(frac3x-1x+2right)=log_3left(fracx+23x-1right)>0.$$
Note that $log_a t>0$ if and only if $t>1$ (when $a>1$).

share|cite|improve this answer

edited Aug 3 at 11:23

amWhy

189k25219431

answered Jul 28 at 16:58

user 108128

19k41544

add a comment | 

up vote
0
down vote

Note:
$$log_frac13(k)>0 text when 0<k<1$$

So you want when:
$$0<frac3x-1x+2<1$$
$$to0^2<frac(3x-1)^2(x+2)^2<1^2$$
$$to0^2(x+2)^2<(3x-1)^2<1^2(x+2)^2$$
$$to0<(3x-1)^2<(x+2)^2$$
Now continue this by finding all $x$ which satisfy:
$$(x+2)^2>(3x-1)^2text AND (3x-1)^2>0$$

share|cite|improve this answer

answered Jul 28 at 17:17

Rhys Hughes

3,8581227

add a comment | 

2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
2
down vote



accepted

Hint:
$$log_(1/3)left(frac3x-1x+2right)=-log_3left(frac3x-1x+2right)=log_3left(fracx+23x-1right)>0.$$
Note that $log_a t>0$ if and only if $t>1$ (when $a>1$).

share|cite|improve this answer

edited Aug 3 at 11:23

amWhy

189k25219431

answered Jul 28 at 16:58

user 108128

19k41544

add a comment | 

up vote
2
down vote



accepted

Hint:
$$log_(1/3)left(frac3x-1x+2right)=-log_3left(frac3x-1x+2right)=log_3left(fracx+23x-1right)>0.$$
Note that $log_a t>0$ if and only if $t>1$ (when $a>1$).

share|cite|improve this answer

edited Aug 3 at 11:23

amWhy

189k25219431

answered Jul 28 at 16:58

user 108128

19k41544

add a comment | 

up vote
2
down vote



accepted

up vote
2
down vote



accepted

Hint:
$$log_(1/3)left(frac3x-1x+2right)=-log_3left(frac3x-1x+2right)=log_3left(fracx+23x-1right)>0.$$
Note that $log_a t>0$ if and only if $t>1$ (when $a>1$).

share|cite|improve this answer

edited Aug 3 at 11:23

amWhy

189k25219431

answered Jul 28 at 16:58

user 108128

19k41544

Hint:
$$log_(1/3)left(frac3x-1x+2right)=-log_3left(frac3x-1x+2right)=log_3left(fracx+23x-1right)>0.$$
Note that $log_a t>0$ if and only if $t>1$ (when $a>1$).

share|cite|improve this answer

edited Aug 3 at 11:23

amWhy

189k25219431

answered Jul 28 at 16:58

user 108128

19k41544

share|cite|improve this answer

share|cite|improve this answer

edited Aug 3 at 11:23

amWhy

189k25219431

edited Aug 3 at 11:23

amWhy

189k25219431

edited Aug 3 at 11:23

amWhy

189k25219431

189k25219431

answered Jul 28 at 16:58

user 108128

19k41544

answered Jul 28 at 16:58

user 108128

19k41544

answered Jul 28 at 16:58

user 108128

19k41544

19k41544

add a comment | 

add a comment | 

up vote
0
down vote

Note:
$$log_frac13(k)>0 text when 0<k<1$$

So you want when:
$$0<frac3x-1x+2<1$$
$$to0^2<frac(3x-1)^2(x+2)^2<1^2$$
$$to0^2(x+2)^2<(3x-1)^2<1^2(x+2)^2$$
$$to0<(3x-1)^2<(x+2)^2$$
Now continue this by finding all $x$ which satisfy:
$$(x+2)^2>(3x-1)^2text AND (3x-1)^2>0$$

share|cite|improve this answer

answered Jul 28 at 17:17

Rhys Hughes

3,8581227

add a comment | 

up vote
0
down vote

Note:
$$log_frac13(k)>0 text when 0<k<1$$

So you want when:
$$0<frac3x-1x+2<1$$
$$to0^2<frac(3x-1)^2(x+2)^2<1^2$$
$$to0^2(x+2)^2<(3x-1)^2<1^2(x+2)^2$$
$$to0<(3x-1)^2<(x+2)^2$$
Now continue this by finding all $x$ which satisfy:
$$(x+2)^2>(3x-1)^2text AND (3x-1)^2>0$$

share|cite|improve this answer

answered Jul 28 at 17:17

Rhys Hughes

3,8581227

add a comment | 

up vote
0
down vote

up vote
0
down vote

Note:
$$log_frac13(k)>0 text when 0<k<1$$

So you want when:
$$0<frac3x-1x+2<1$$
$$to0^2<frac(3x-1)^2(x+2)^2<1^2$$
$$to0^2(x+2)^2<(3x-1)^2<1^2(x+2)^2$$
$$to0<(3x-1)^2<(x+2)^2$$
Now continue this by finding all $x$ which satisfy:
$$(x+2)^2>(3x-1)^2text AND (3x-1)^2>0$$

share|cite|improve this answer

answered Jul 28 at 17:17

Rhys Hughes

3,8581227

Note:
$$log_frac13(k)>0 text when 0<k<1$$

So you want when:
$$0<frac3x-1x+2<1$$
$$to0^2<frac(3x-1)^2(x+2)^2<1^2$$
$$to0^2(x+2)^2<(3x-1)^2<1^2(x+2)^2$$
$$to0<(3x-1)^2<(x+2)^2$$
Now continue this by finding all $x$ which satisfy:
$$(x+2)^2>(3x-1)^2text AND (3x-1)^2>0$$

share|cite|improve this answer

answered Jul 28 at 17:17

Rhys Hughes

3,8581227

share|cite|improve this answer

share|cite|improve this answer

answered Jul 28 at 17:17

Rhys Hughes

3,8581227

answered Jul 28 at 17:17

Rhys Hughes

3,8581227

answered Jul 28 at 17:17

Rhys Hughes

3,8581227

3,8581227

add a comment | 

add a comment |