Step 1 :The question is asking for the equivalent logarithmic form of the exponential equation $10^{z}=0.6$. The general form of a logarithm is $\log_b(a) = c$, which is equivalent to $b^c = a$. Therefore, we need to find the form that matches this pattern.
Step 2 :The equivalent logarithmic form of the exponential equation $10^{z}=0.6$ is $\log _{10}(0.6)=z$.
Step 3 :Final Answer: $\boxed{\log _{10}(0.6)=z}$