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- Find the derivative using the definition
- Solve by quadratic formula (general formula)
- Simplify
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- Find the derivative
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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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$\frac{\log \left(\frac{1}{8}\right)}{\log \left(x\right)}=-3$
Learn how to solve problems step by step online. Solve the logarithmic equation logx(1/8)=-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.
