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Popular >

simplify log_{sqrt(5)}(5)

Solution

simplify

lo g_{5} (5)

Solution

2

Solution steps

lo g_{5} (5)

Apply radical rule:

a = a^{\frac{1}{2}}

5 = 5^{\frac{1}{2}}

= lo g_{5^{\frac{1}{2}}} (5)

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{5^{\frac{1}{2}}} (5) = \frac{1}{\frac{1}{2}} lo g_{5} (5)

= \frac{1}{\frac{1}{2}} lo g_{5} (5)

Apply log rule:

lo g_{a} (a) = 1

lo g_{5} (5) = 1

= \frac{1}{\frac{1}{2}} \cdot 1

\frac{1}{\frac{1}{2}} \cdot 1 = 2

= 2

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Frequently Asked Questions (FAQ)

What is log_{sqrt(5)}(5) ?
The solution to log_{sqrt(5)}(5) is 2