Exercise
16^{\log_{\frac{1}{8}}125}=
Final Answer
Solution
Using Logarithm Rules we get:
16^{\log_{\frac{1}{8}}125}=
=16^{\log_{2^{-3}}125}=
=16^{\log_{2^{-3}}5^3}=
=16^{\frac{\log_2 5^3}{\log_2 2^{-3}}}=
=16^{\frac{\log_2 5^3}{-3}}=
=16^{-\frac{1}{3}\log_2 5^3}=
=16^{3\cdot (-\frac{1}{3})\log_2 5}=
=16^{-\log_2 5}=
=16^{\log_2 5^{-1}}=
=2^{4\log_2 5^{-1}}=
=2^{\log_2 5^{-4}}=
=5^{-4}=
=\frac{1}{5^{-4}}=
=\frac{1}{625}=