Answer
This equation has no solutions
Work Step by Step
$\ln(x-2)+\ln3=\ln(5x-7)$
Combine the sum on the left side of the equation as the logarithm of a product:
$\ln3(x-2)=\ln(5x-7)$
Evaluate the product inside the $\ln$ on the left side:
$\ln(3x-6)=\ln(5x-7)$
If $\ln(3x-6)=\ln(5x-7)$, then $3x-6=5x-7$
$3x-6=5x-7$
Solve for $x$:
$3x-5x=-7+6$
$-2x=-1$
$x=\dfrac{1}{2}$
Check the solution found by plugging them into the original equation:
$\ln\Big(\dfrac{1}{2}-2\Big)+\ln3=\ln\Big[5\Big(\dfrac{1}{2}\Big)-7\Big]$ False
This equation has no solutions
