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Popular >

simplify log_{sqrt(2)}(x)

Solution

simplify

lo g_{2} (x)

Solution

2 lo g_{2} (x)

Solution steps

lo g_{2} (x)

Apply radical rule:

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

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

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

Apply log rule:

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

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

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

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

= 2 lo g_{2} (x)

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Frequently Asked Questions (FAQ)

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