Help with Logarithmic Function?

Question

anonymous · Answer

attachment

ranga · Answer

Take logarithm on both sides. Make use of the fact that log(A)^N = N * log(A)
Solve for x.

jdoe0001 · Answer

$\bf 8^x=60\ \quad \ \quad \
\textit{log cancellation rule of }\quad \color{blue}{log_aa^x=x}\qquad thus\ \quad \
8^x=60\implies log_88^x=log_860\implies x=log_860\ \quad \
\textit{change of base rule of}\quad \color{blue}{log_ab=\cfrac{log_cb}{log_ca}}\qquad thus\ \quad \
x=log_860\implies \cfrac{log_{10}60}{log_{10}8}$

anonymous · Answer

That's not one of the options, not even when simplified with a calculator

jdoe0001 · Answer

well. then it should be, because that's the proper result

anonymous · Answer

So which one should I put?

jdoe0001 · Answer

hmmm... good one.. can't say... I do know that the procedure is proper though.... lemme show you in wolfram site http://www.wolframalpha.com/input/?i=8%5Ex%3D60

anonymous · Answer

Yeah, I know, logarithms are nothing new to me, my dilemma was to put an answer. I took a screenshot and I'm telling my teacher the question did not have the right answer.

ranga · Answer

You can clearly see x must be less than 2 because at x = 2 it is 64 which exceeds the right hand side value.  The correct answer is not among the given choices.