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

Logarithm Rules – Exercise 987

Exercise

\sqrt{5^{2+\frac{1}{2}\log_5 16}}=

Final Answer

\sqrt{5^{2+\frac{1}{2}\log_5 16}}=10

Solution

Using Logarithm Rules we get:

\sqrt{5^{2+\frac{1}{2}\log_5 16}}=

=\sqrt{5^2\cdot 5^{\frac{1}{2}\log_5 16}}=

=\sqrt{5^2\cdot 5^{\log_5 16^{\frac{1}{2}}}}=

=\sqrt{25\cdot 5^{\log_5 4}}=

=\sqrt{25\cdot 4}=

=\sqrt{100}=10

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