Rewrite functions in equivalent forms to reveal and explain useful properties.
Convert exponential and logarithmic forms and solve
Problem
Convert \(2^x~=~8\) to logarithmic form, solve for \(x\), and check the result in the original equation.
Big Picture
What this problem is really about
Label the three roles in the exponential equation before converting: the base stays the logarithmic base, the exponential result becomes the logarithm’s argument, and the exponent becomes the logarithm’s output. Then recognize the argument as a power of the base to solve. Substitution into the original exponential equation provides the quickest check that no roles were reversed.
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