Logarithm Rules – Exercise 987

Exercise

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

Final Answer

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Solution

Using Logarithm Rules we get:

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

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

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

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

$=\sqrt{25\cdot 4}=$

$=\sqrt{100}=10$