Question 417262
I assume "log4 x" means {{{log(4, (x))}}}.<br>
{{{g(8) = log(4, ((8)))}}}
Since 4, the base, and 8, the argument, are both powers of 2 ({{{4 = 2^2}}} and {{{8 = 2^3}}}), we will be able find find this logarithm without the use of a calculator. We will use the change of base formula, {{{log(a, (p)) = log(b, (p))/log(b, (a))}}}, to convert this base 4 log into an expression of base 2 logs:
{{{g(8) = log(4, ((8))) = log(2, (8))/log(2, (4)) = 3/2}}}