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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
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$\frac{\log \left(x\right)}{\log \left(8\right)}=\frac{1}{3}$
Learn how to solve problems step by step online. Solve the logarithmic equation log8(x)=1/3. 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. 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. 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.
