Write the following exponential equation as an equivalent logarithmic equation:
\[
w^{-5}=r
\]

The equivalent equation is: $\log _{w}(\square)=\square$.
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Answer

The equivalent logarithmic equation is $ \boxed{\log _{w}(r)=-5} $.

Steps

Step 1 ：The given equation is in the form of an exponential equation, where the base is 'w', the exponent is '-5' and the result is 'r'.

Step 2 ：The equivalent logarithmic equation would be in the form of log_base(result) = exponent.

Step 3 ：So, we need to substitute 'w' as the base, 'r' as the result and '-5' as the exponent in the logarithmic equation.

Step 4 ：The equivalent logarithmic equation is $ \boxed{\log _{w}(r)=-5} $.