**log**since we know that when the log

_{3}_{3}a = log

_{3}b, then very simply a must be equal to b. In this problem a=3x-6 and b=2x+1

**x=7**

solve the equation log3 (3x-6) = log3 (2x+1)

Tutors, sign in to answer this question.

George T. | George T.--"It's All About Math!"George T.--"It's All About Math!"

Heather:

In this problem, you shouldn't be confused by the **log**_{3}
since we know that when the log_{3} a = log_{3} b, then very simply a must be equal to b. In this problem a=3x-6 and b=2x+1

So: 3x-6=2x+1

3x-2x=1+6

1x=7

Hope this helps!

George T.

Hi Heather;

log_{3} (3x-6) = log_{3} (2x+1)

Before I answer this, I was like to briefly review logarithms.

Let's just say that...

log_{3} (3x-6) = 5

I randomly selected the number 5.

This would resolve as...

3x-6=3^{5}

Do you see how the base _{3} moved to the other side of the = sign and became a 3, whereas the 5 rose to exponential status of
^{5}?

I love the way Megan described the components as base, exponent and "answer". If she does not mind, I intend to use it in future answers.

In the equation you provided, the base of _{3} appears on both sides of the equation. Henceforth...

log_{3} (3x-6) = log_{3} (2x+1)

we can cancel these.

3x-6=2x+1

Let's add 6 to both sides as we proceed to isolate x...

3x-6+6=2x+1+6

3x=2x+7

Let's subtract 2x from both sides...

-2x+3x=2x+7-2x

x=7

Let's verify...

(3x-6) ??? (2x+1)

[3(7)-6] ??? [2(7)+1]

21-6 ??? 14+1

15=15

All Good!

Megan H. | Math Tutoring - All GradesMath Tutoring - All Grades

Hey Heather!

log_{3}9=2 -->example

3 is the base, 2 is the exponent and 9 is what I call the answer. You can rewrite this expression as 3^{2}=9 so you can see that. In the expression you have both of your logs have the same base of 3 and since they are set equal to each other tell you that they must have the same exponent. Therefore the answers must be equal so you can just set 3x-6=2x+1 and solve for x.

In this similar problem:

log2(2x-2)=log2(x+1)

2x-2 = x+1 -->set answers equal to eachother

x-2=1 --> solve for x

x=3

Good Luck!

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Glynis S.

Let me help you tutoring service.

$12.50 per 15 min

View Profile >

Dolores A.

30 years Elem Reading, Grammar,Writing, Teacher, Author, MA Degree

$10 per 15 min

View Profile >

Randee S.

Dynamic, versatile tutor for core subject areas K-12

$8.75 per 15 min

View Profile >