Question

Solve for x and express your answer as a logarithm.

Answer 1

$2\cdot10^{3x}=24\ \ \ \ |divide\ both\ sides\ by\ 2\\\\10^{3x}=12\iff\log(10^{3x})=\log(12)\\\\3x\log(10)=\log(12)\\\\3x=\log(12)\ \ \ \ |divide\ both\ sides\ by\ 3\\\\\boxed{x=\frac{\log(12)}{3}}\to\dfrac{\log(12)}{3}=\dfrac{1}{3}\log(12)=\log\left(12^\frac{1}{3}\right)=\boxed{\log\sqrt[3]{12}}$

$Use:\\\log_ab^c=c\log_ab\\\log_aa=1\\a^\frac{1}{n}=\sqrt[n]{a}\\-------------------\\\\Answer:\boxed{x=\frac{\log(12)}{3}\ other\ form\ x=\log(\sqrt[3]{12})}$