Question

the value of log 512 to the base 64

Answer 1

Answer:

$log_{64}512=\frac{3}{2}$

Step-by-step explanation:

Formula used:

If$\:N=a^x$

Then, $log_aN=x$

Given:

$Let,x=log_{64}512$

$x=log_{64}512$

$(64)^x=512$

$(2^6)^x=2^9$

$2^{6x}=2^9$

$6x=9$

$x=\frac{9}{6}$

$x=\frac{3}{2}$

$\implies\:log_{64}512=\frac{3}{2}$