Question 545712
log base5(sqrt 125)= x 
write the exponent equiv of logs
{{{5^x = sqrt(125)}}}
Square both sides
{{{5^(2x) = 125}}}
using common logs
{{{log((5^(2x))) = log((125))}}}
which is
2x * log(5) = log(125)
2x = {{{log(125)/log(5)}}}
use a calc
2x = 3
x = 1.5
:
:
check this on a calc
enter 5^1.5 = 11.18
enter {{{sqrt(125)}}} = 11.18