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Popular >

simplify log_{sqrt(5)}(25)

Solution

simplify

lo g_{5} (25)

Solution

4

Solution steps

lo g_{5} (25)

Apply radical rule:

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

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

= lo g_{5^{\frac{1}{2}}} (25)

Apply log rule:

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

lo g_{5^{\frac{1}{2}}} (25) = \frac{1}{\frac{1}{2}} lo g_{5} (25)

= \frac{1}{\frac{1}{2}} lo g_{5} (25)

Factor the number:

25 = 5^{2}

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

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{5} (5^{2}) = 2

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

\frac{1}{\frac{1}{2}} \cdot 2 = 4

= 4

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simplify ((2^{-10})/(4^2))^7 simplify

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Frequently Asked Questions (FAQ)

What is log_{sqrt(5)}(25) ?
The solution to log_{sqrt(5)}(25) is 4