I'm stuck on a problem: log

_{2}(2x+6)-log_{2}(x-1)=log_{2}3I haven't learned how to do it, and I can't seem to find an example or a step-by-step. Please help!

I'm stuck on a problem: log_{2}(2x+6)-log_{2}(x-1)=log_{2}3

I haven't learned how to do it, and I can't seem to find an example or a step-by-step. Please help!

Tutors, please sign in to answer this question.

Woodland Hills, CA

What is important to realize is that:

Log ( AB) = log A + Log B

Log A/ B = Log A - Log B

Log_{2} ( 2X +6) - Log _{2 }( X - 2) = Log_{2} 3

Log_{2 [ ( 2X - 6) / X -1 )] = }Log_{2} 3

(2X + 6 / X - 1) = 3

3X -3 = 2 X + 6

X = 9

It will be Good Exercise to do the following calculations:

Log_{6} 9 + Log_{6} 4 =

Log_{3} 27 + Log_{3} 3 =

Log _{2 }8 + Log_{2} 2 =

Chicago, IL

1. Use the relationship log_{x}a - log_{x}b = log_{x}(a/b)

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

⇒ log_{2}((2x+6)/(x-1)) = log_{2}3

2. Use the relationship that log_{x}a = log_{x}b implies a = b

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

⇒ (2x+6)/(x-1) = 3

3. Multiply both sides by x-1

(2x+6)/(x-1) = 3

⇒ 2x+6 = 3(x-1)

4. Solve for x

2x+6 = 3(x-1)

⇒ 2x+6 = 3x-3

⇒ 9 = x

So x=9.

Middletown, CT

Hi Jensen;

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

Our first priority is to verify that all logs are to the same base. These are all to the base of 2. We may now proceed.

The logarithm-principle we need to apply is...

log a/b=log a - log b

Therefore...

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

We can eliminate log_{2} on both sides...

(2x+6)/(x-1)=3

(2x+6)/(x-1)=3/1

Let's cross-multiply...

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

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

2x+6=3x-3

Let's combine like terms...

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

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

6=x-3

Let's add 3 to both sides...

3+6=x-3+3

Let's check our work by returning to the original equation...

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

log_{2}[(2*9)+6)-log_{2}(9-1)=log_{2}3

log_{2}(18+6)-log_{2}(8)=log_{2}3

log_{2}(24)-log_{2}(8)=log_{2}3

log a/b=log a - log b

log_{2}[(24)/(8)]=log_{2}3

log_{2}3=log_{2}3

Jing X.

IVY-graduate specializing in SAT, ACT, Math and College App

Brooklyn, NY

4.9
(76 ratings)

Charles P.

College and Test Prep Tutor: IB Papers, GRE, GMAT, MCAT, SAT, AP Exams

New York, NY

5.0
(490 ratings)

Jeffrey G.

Former Med-Student turned Professional Science Tutor

Brooklyn, NY

5.0
(368 ratings)

- Algebra 2 3240
- Algebra 4727
- Math 9021
- Math Help 5028
- College Algebra 1007
- Logarithmic Functions 86
- Logarithmic Identities 1
- Logarithmic Equation 76
- Calculus 2085
- Precalculus 1444