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

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.

• Hi Esha;I think you need to develop some writing skills before posting a question – Learnmore Apr 9 '17 at 2:43
• I am also new but that's what the tour page says – Learnmore Apr 9 '17 at 2:43
• Check out the following link for math formatting tips: math.meta.stackexchange.com/questions/5020/… – Dave Apr 9 '17 at 2:44
• thanx for showing me this. its really a huge help. do i need to repost this question again? – Esha Mukhopadhyay Apr 9 '17 at 2:46
• please pardon me and help me in this question . ill try my best in the future ones – Esha Mukhopadhyay Apr 9 '17 at 2:47

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