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Popular >

simplify log_{sqrt(4)}(8)

Solution

simplify

lo g_{4} (8)

Solution

3

Solution steps

lo g_{4} (8)

Factor

4 : 2^{1}

= lo g_{2^{1}} (8)

Apply log rule:

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

lo g_{2^{1}} (8) = \frac{1}{1} lo g_{2} (8)

= \frac{1}{1} lo g_{2} (8)

\frac{1}{1} lo g_{2} (8) = lo g_{2} (8)

= lo g_{2} (8)

Factor the number:

8 = 2^{3}

= lo g_{2} (2^{3})

Apply log rule:

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

= 3

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Frequently Asked Questions (FAQ)

What is log_{sqrt(4)}(8) ?
The solution to log_{sqrt(4)}(8) is 3