# How do you simplify 5^[log_5 (6) + log_5 (7)]?

Mar 20, 2016

The operation $\left({a}^{{\log}_{a}}\right)$ is successively an operation and its inverse operation. This is equivalent to multiplication by 1.
So, ${a}^{{\log}_{a} x} = x$.
Here, ${5}^{{\log}_{5} \left(6\right) + {\log}_{5} \left(7\right)} = {5}^{{\log}_{5} \left(42\right)} = 42$.