Question

If log(x+3)-log(x-5)=log2

What is the value of x?

Please answer with explanation and process

Answer 1

We use log(x) - log(y) = log(x/y) and log(x) = log(y) ⇔ x = y


`\displaystyle\log(x+3) - \log(x-5) = \log 2 \implies \log\left( (x+3)/(x-5) \right) = \log 2 \implies \\ \\ (x+3)/(x-5) = 2 \implies x+3 = 2(x-5) \\ \\ x = 13`