Question 421639
We have {{{log(8, 2x^2) + log(8, 4) = 5}}}. We can use the formula {{{log(a,x) + log(a,y) = log(a,xy)}}} to obtain


{{{log(8, 8x^2) = 5}}}


Raise each side to the exponent with base 8, i.e. {{{8^(log(8, 8x^2)) = 8^5}}} to get


{{{8x^2 = 8^5}}}


{{{x^2 = 8^4}}}


x = 64 or -64. We have to be especially careful dealing with negative solutions or obtaining a negative in the logarithm, since the logarithm is not defined on negative numbers (disregarding complex values). We can check that both solutions satisfy.