Question

what is the log(45)/log(15) simplified?

Answer 1

$\frac{log(45)}{log{(15)}} = \frac{log(9 * 5)}{log{(3 * 5)}} = \frac{log(9) + log(5)}{log(3) + log(5)} = \frac{log(3^{2}) + log(5)}{log(3) + log(5)} = \frac{2log(3) + log(5)}{log(3) + log(5)} = \frac{2log(3)}{log(3) + log(5)} + \frac{log(5)}{log(3) + log(5)}$

Answer 2

Sorry...I completely goofed on my previous answer. You could do what Panoyin did, but you could also remember that logbase(a)x = logbaseb(x)/logbaseb(a). Therefore, log(45)/log(15) can simplify to logbase15(45)