The simplified value of $\log_a \!\sqrt[m]{a^m \cdot \sqrt[n]{a^n}}$-style expression $\log_a \sqrt[m]{(a^m)\sqrt[n]{a^n

Question

The simplified value of $\log_a \!\sqrt[m]{a^m \cdot \sqrt[n]{a^n}}$-style expression $\log_a \sqrt[m]{(a^m)\sqrt[n]{a^n}}$ reduces to:

Accepted Answer

$1 + \dfrac{1}{mn}$

Answer

$0$

Answer

$1 + \dfrac{1}{n}$

Answer

$\dfrac{1}{mn}$

The simplified value of log⁡a ⁣am⋅annm\log_a \!\sqrt[m]{a^m \cdot \sqrt[n]{a^n}}loga​mam⋅nan-style expression log⁡a(am)annm\log_a \sqrt[m]{(a^m)\sqrt[n]{a^n}}loga​m(am) reduces to: