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Popular >

simplify log_{sqrt(2)}(32)

Solution

simplify

lo g_{2} (32)

Solution

10

Solution steps

lo g_{2} (32)

Apply radical rule:

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

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

= lo g_{2^{\frac{1}{2}}} (32)

Apply log rule:

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

lo g_{2^{\frac{1}{2}}} (32) = \frac{1}{\frac{1}{2}} lo g_{2} (32)

= \frac{1}{\frac{1}{2}} lo g_{2} (32)

Factor the number:

32 = 2^{5}

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

Apply log rule:

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

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

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

\frac{1}{\frac{1}{2}} \cdot 5 = 10

= 10

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Frequently Asked Questions (FAQ)

What is log_{sqrt(2)}(32) ?
The solution to log_{sqrt(2)}(32) is 10