Learn how to solve problems step by step online. Solve the logarithmic equation log1/3(x)=-2. 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. Multiply both sides of the equation by \log \left(\frac{1}{3}\right). Apply the formula: a\log_{b}\left(x\right)=\log_{b}\left(x^a\right), where a=-2, b=10 and x=\frac{1}{3}. Since the exponent is negative, we can invert the fraction.

Solve the logarithmic equation log1/3(x)=-2