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Popular >

expand log_{8}(32)

Solution

expand

lo g_{8} (32)

Solution

\frac{5}{3}

+1

Solution steps

lo g_{8} (32)

Rewrite

8

as

2^{3}

= lo g_{2^{3}} (32)

Apply log rule:

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

lo g_{2^{3}} (32) = \frac{1}{3} lo g_{2} (32)

= \frac{1}{3} lo g_{2} (32)

Rewrite

32

in power-base form:

32 = 2^{5}

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

Apply log rule:

lo g_{a} (a) = 1

lo g_{2} (2) = 1

= \frac{1}{3} \cdot 5 \cdot 1

\frac{1}{3} \cdot 5 \cdot 1 = \frac{5}{3}

= \frac{5}{3}

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Frequently Asked Questions (FAQ)

What is expand log_{8}(32) ?
The solution to expand log_{8}(32) is 5/3