# logarithm problem

• Mar 1st 2010, 05:56 AM
mastermin346
logarithm problem
how to solve this question

$

2+\log_2{(3x-1)}=\log_2{4x}
$
• Mar 1st 2010, 06:14 AM
earboth
Quote:

Originally Posted by mastermin346
how to solve this question

$

2+\log_2{(3x-1)}=\log_2{4x}
$

1. Re-write the equation:

$2+\log_2{(3x-1)}=\log_2{4x}~\implies~2=\log_2{4x} - \log_2{(3x-1)}~\implies~$ $2=\log_2\left( \frac{4x}{(3x-1)}\right)$

2. Now use the base 2 on both sides of the equation:

$4=\frac{4x}{(3x-1)}$ Solve for x. Keep in mind that $x > \tfrac13$.