Question

PLEASE SOLVE the following attached question

Answer 1

$log_3|2x-7|=4\\ \\ \Rightarrow |2x-7|=3^4\\ \\ \Rightarrow |2x-7|=81\\ \\ \Rightarrow 2x-7= \pm 81\\ \\ \Rightarrow 2x=7 \pm 81$

$\Rightarrow 2x=7+81\ or\ 7-81\\ \\ \Rightarrow 2x=88\ or\ -74\\ \\\Rightarrow x= \frac{88}{2} \ or\ \frac{-74}{2} \\ \\ \Rightarrow x=44\ or\ -37$

Answer 2

given $log_{3}|2x-7| = 4$

|2x - 7| = $3^{4}$
| 2x - 7 | = 81

2x - 7 = 81    or 2x - 7 = -81

2x = 88   or   2x = - 74

x = 44   or  x = -37