how to solve this logarithamic term? $a^{\log_{\frac1a}{\frac12}}$

Question

the question : $$a^{\log_{\frac1a}{\frac12}}$$ relevant equation : $$a^ {\log_a(x)} = x$$ $$\log_{c^m} (y) =\frac1m \log_c{(y)}$$ my try at it :
I first changed the base into a by multiplying the log part by $(-1)$. the answer was $a^{ - \log_a{\frac12}}.$ this is equal to $\dfrac{a^1}{\log_a\left(\frac12\right)}$. please help me after that.

Answer 1

Answer: $2.$

Proof: Let $z = \log_{1/a}(1/2) = \frac{\log_a (1/2)}{\log_a (1/a)} = - \log_a (1/2).$

Then $a^z = a^{- \log_a (1/2)} =$ $\frac {1} {a^{\log_a (1/2)}} =$ $\frac {1} {1/2} = 2.$