find the exact value of the logarithm without using a calcul

find the exact value of the logarithm without using a calculator

log (base 4) 256 ___ type an integer or simplified fraction

Solution

log (base 4) 256

256 is 4^4 so we have

log(base4) of 4^4 = x

This in exponential form is :
4^x = 4^4

So, x = 4

Thus, the value of that is 4