Answer
No solution or $\varnothing $.
Work Step by Step
The given equation is
$\log (3x-5) -\log (5x)=2$
Use quotient rule.
$\log \left [\frac{3x-5}{5x} \right]=2$
Rewrite the common logarithm showing base $10$.
$\log_{10} \left [\frac{3x-5}{5x} \right]=2$
Rewrite in exponential form.
$\frac{3x-5}{5x}= 10^2$
Multiply both sides by $5x$.
$(5x)\cdot \frac{3x-5}{5x}= (5x)\cdot 100$
Clear the parentheses.
$3x-5=500x$
Add $-3x$ to both sides.
$3x-5-3x=500x-3x$
Simplify.
$-5=497x$
Divide both sides by $497$.
$-\frac{5}{497}=\frac{497x}{497}$
Simplify.
$-\frac{5}{497}=x$
Negative values are not defined for log functions.