Question

Which of the following is equivalent to log 4 32 ?

Answer 1

The answer is 5/2

$log_x(y) = \frac{log(y)}{log(x)} \\ log_4(32) = \frac{log(32)}{log(4)}$

$log (x^{a}) =a*log(x) \\ log(32)= log( 2^{5})=5*log(2) \\ log(4)= log( 2^{2})=2*log(2)$

$\frac{log(32)}{log(4)}= \frac{5*log(2)}{2*log(2)} = \frac{5}{2}$