## Precalculus: Mathematics for Calculus, 7th Edition

$\ln(x-2)+\ln3=\ln(5x-7)$ 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