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Popular >

simplify log_{sqrt(8)}(4)

Solution

simplify

lo g_{8} (4)

Solution

\frac{4}{3}

+1

Decimal Notation

1.33333 \dots

Solution steps

lo g_{8} (4)

Factor

8 : 2^{\frac{3}{2}}

= lo g_{2^{\frac{3}{2}}} (4)

Apply log rule:

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

lo g_{2^{\frac{3}{2}}} (4) = \frac{1}{\frac{3}{2}} lo g_{2} (4)

= \frac{1}{\frac{3}{2}} lo g_{2} (4)

Factor the number:

4 = 2^{2}

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

Apply log rule:

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

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

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

\frac{1}{\frac{3}{2}} \cdot 2 = \frac{4}{3}

= \frac{4}{3}

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Frequently Asked Questions (FAQ)

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