Question

solve. log2(7x+1)=log2(2-x)

Answer 1

7x+1=2-x
The answer is x=1/8

Answer 2

$\log _{10}\left(2\right)\left(7x+1\right)=\log _{10}\left(2\right)\left(2-x\right)$
Expand:
$7x\log _{10}\left(2\right)+\log _{10}\left(2\right)=2\log _{10}\left(2\right)-x\log _{10}\left(2\right)$
$7x\log _{10}\left(2\right)=-x\log _{10}\left(2\right)+\log _{10}\left(2\right)$
$8x\log _{10}\left(2\right)=\log _{10}\left(2\right)$
$\frac{8x\log _{10}\left(2\right)}{8\log _{10}\left(2\right)}=\frac{\log _{10}\left(2\right)}{8\log _{10}\left(2\right)}$
So:
$x=\frac{1}{8}$