Learn how to solve problems step by step online. Solve the logarithmic equation logx(1/64)=-3. Change the logarithm to base 10 applying the change of base formula for logarithms: \log_b(a)=\frac{\log_{10}(a)}{\log_{10}(b)}. Since \log_{10}(b)=\log(b), we don't need to write the 10 as base. Take the reciprocal of both sides of the equation. Apply fraction cross-multiplication. Apply the formula: a\log_{b}\left(x\right)=\log_{b}\left(x^a\right), where a=-3 and b=10.

Solve the logarithmic equation logx(1/64)=-3