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Popular >

simplify log_{16}(128)

Solution

simplify

lo g_{16} (128)

Solution

\frac{7}{4}

+1

Decimal Notation

1.75

Solution steps

lo g_{16} (128)

Factor the number:

16 = 2^{4}

= lo g_{2^{4}} (128)

Apply log rule:

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

lo g_{2^{4}} (128) = \frac{1}{4} lo g_{2} (128)

= \frac{1}{4} lo g_{2} (128)

Factor the number:

128 = 2^{7}

= \frac{1}{4} lo g_{2} (2^{7})

Apply log rule:

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

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

= \frac{1}{4} \cdot 7

\frac{1}{4} \cdot 7 = \frac{7}{4}

= \frac{7}{4}

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Frequently Asked Questions (FAQ)

What is log_{16}(128) ?
The solution to log_{16}(128) is 7/4