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Popular >

simplify 3log_{32}(2)

Solution

simplify

3 lo g_{32} (2)

Solution

\frac{3}{5}

+1

Decimal Notation

0.6

Solution steps

3 lo g_{32} (2)

Factor the number:

32 = 2^{5}

= 3 lo g_{2^{5}} (2)

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (a) = 1

lo g_{2} (2) = 1

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

Multiply the numbers:

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

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

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

= \frac{3}{5}

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Frequently Asked Questions (FAQ)

What is 3log_{32}(2) ?
The solution to 3log_{32}(2) is 3/5