Final answer to the problem
Step-by-step Solution
Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation log16(x)=1/2. 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. Apply fraction cross-multiplication. Apply the formula: a\log_{b}\left(x\right)=\log_{b}\left(x^a\right), where a=2 and b=10. For two logarithms of the same base to be equal, their arguments must be equal. In other words, if \log(a)=\log(b) then a must equal b.