Question 374721
Remember that we can rewrite {{{log(b,(x))=y}}} as {{{x=b^y}}}



So this means that we can rewrite {{{log(64,(x))=-1/6}}} as {{{x=64^(-1/6)^""}}}



{{{x=64^(-1/6)^""}}} Start with the given equation.



{{{x=(2^6)^(-1/6)^""}}} Rewrite {{{64}}} as {{{2^6}}}



{{{x=2^(6(-1/6))^""}}} Use the identity {{{(x^(y))^z=x^(y*z)}}}



{{{x=2^(-6/6)^""}}} Multiply



{{{x=2^(-1)}}} Reduce.



{{{x=1/2^(1)}}} Flip the base to make the exponent positive.



{{{x=1/2}}} Evaluate {{{2^1}}} to get 2.



So the solution is {{{x=1/2}}}



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