Given-that-log-3x-1-2x-1-log-3x-1-5-find-the-value-of-x-

Question Number 54875 by shaddie last updated on 13/Feb/19

Given that \frac{\log {(3 x + 1)}^{2 x - 1}}{\log (3 x + 1)} = 5, find the value of x .

Answered by kaivan.ahmadi last updated on 14/Feb/19

\log {(3 x + 1)}^{2 x - 1} = \log {(3 x + 1)}^{5} \Rightarrow

{(3 x + 1)}^{2 x - 1} = {(3 x + 1)}^{5} \Rightarrow 2 x - 1 = 5 \Rightarrow

x = 3

Answered by Otchere Abdullai last updated on 14/Feb/19

s o l u t i o n

\frac{l o g {(3 x + 1)}^{2 x - 1}}{l o g (3 x + 1)} = 5

\Rightarrow \frac{(2 x - 1) l o g (3 x + 1)}{l o g (3 x + 1)} = 5

\Rightarrow 2 x - 1 = 5

\Rightarrow 2 x = 5 + 1

\Rightarrow 2 x = 6

\Rightarrow \frac{2 x}{2} = \frac{6}{2}

\Rightarrow x = 3