fbpx
calculus online - Free exercises and solutions to help you succeed!

Logarithm Rules – Exercise 991

Exercise

16^{\log_{\frac{1}{8}}125}=

Final Answer

16^{\log_{\frac{1}{8}}125}=\frac{1}{625}

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}=

Share with Friends

Leave a Reply