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Popular >

simplify log_{sqrt(5)}(125)

Solution

simplify

lo g_{5} (125)

Solution

6

Solution steps

lo g_{5} (125)

Apply radical rule:

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

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

= lo g_{5^{\frac{1}{2}}} (125)

Apply log rule:

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

lo g_{5^{\frac{1}{2}}} (125) = \frac{1}{\frac{1}{2}} lo g_{5} (125)

= \frac{1}{\frac{1}{2}} lo g_{5} (125)

Factor the number:

125 = 5^{3}

= \frac{1}{\frac{1}{2}} lo g_{5} (5^{3})

Apply log rule:

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

lo g_{5} (5^{3}) = 3

= \frac{1}{\frac{1}{2}} \cdot 3

\frac{1}{\frac{1}{2}} \cdot 3 = 6

= 6

Popular Examples

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Frequently Asked Questions (FAQ)

What is log_{sqrt(5)}(125) ?
The solution to log_{sqrt(5)}(125) is 6