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Popular >

simplify log_{128}(32)

Solution

simplify

lo g_{128} (32)

Solution

\frac{5}{7}

+1

Decimal Notation

0.71428 \dots

Solution steps

lo g_{128} (32)

Factor the number:

128 = 2^{7}

= lo g_{2^{7}} (32)

Apply log rule:

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

lo g_{2^{7}} (32) = \frac{1}{7} lo g_{2} (32)

= \frac{1}{7} lo g_{2} (32)

Factor the number:

32 = 2^{5}

= \frac{1}{7} lo g_{2} (2^{5})

Apply log rule:

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

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

= \frac{1}{7} \cdot 5

\frac{1}{7} \cdot 5 = \frac{5}{7}

= \frac{5}{7}

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Frequently Asked Questions (FAQ)

What is log_{128}(32) ?
The solution to log_{128}(32) is 5/7