Solve 2 log <mrow class="MJX-TeXAtom-ORD"> 3 </mrow> </msub> &#x

Edith Mayer

Edith Mayer

Answered question

2022-04-10

Solve 2 log 3 ( x ) log 3 ( x + 6 ) = 1
just getting going with logarithms, having trouble with this question.
2 log 3 ( x ) log 3 ( x + 6 ) = 1
log 3 x 2 log 3 ( x + 6 ) = 1
Stuck at this point: What do I do next?
log 3 ( x 2 x + 6 ) = 1
Edit: Got it!
x 2 x + 6 = 3 1
x 2 x + 6 = 3
x 2 = 3 ( x + 6 )
x 2 = 3 x + 18
x 2 3 x 18 = 0
( x 6 ) ( x + 3 ) = 0
x = 6 and cannot equal 3 as 2 log 3 ( 3 ) < 0

Answer & Explanation

Carolyn Farmer

Carolyn Farmer

Beginner2022-04-11Added 16 answers

Good so far. Now use the property that
log 3 a = b a = 3 b
This leads to
x 2 x + 6 = 3
Rearranging, this is a quadratic equation.
vilitatelp014

vilitatelp014

Beginner2022-04-12Added 6 answers

To get x out of logarithm, you raise the base (3) with the logarithm (as log and exponent are inverses)
log 3 ( x 2 x + 6 ) = 1
3 log 3 ( x 2 x + 6 ) = 3 1
x 2 x + 6 = 3
then solve the quadratic to get x value

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?