Question

Solve for $x$: $\log (5x+2)-\log 7=\log (x-2)$

Answer 1

Consider the given equation.

$\log (5x+2)-\log 7=\log (x-2)$

$\log \left(\frac{5x+2}{7}\right)=\log (x-2)$ $\because \log m-\log n=\log \frac{m}{n}$

$\frac{5x+2}{7}=x-2$

$5x+2=7x-14$

$2x=16$

$x=8$.