What is expand log_{64}(16) ?

The solution to expand log_{64}(16) is 2/3

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expand log_{64}(16)

expand

lo g_{64} (16)

\frac{2}{3}

Decimal Notation

0.66666 \dots

Solution steps

lo g_{64} (16)

Rewrite

64

2^{6}

= lo g_{2^{6}} (16)

Apply log rule:

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

lo g_{2^{6}} (16) = \frac{1}{6} lo g_{2} (16)

= \frac{1}{6} lo g_{2} (16)

Rewrite

16

in power-base form:

16 = 2^{4}

= \frac{1}{6} lo g_{2} (2^{4})

Apply log rule:

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

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

= \frac{1}{6} \cdot 4 lo g_{2} (2)

Apply log rule:

lo g_{a} (a) = 1

lo g_{2} (2) = 1

= \frac{1}{6} \cdot 4 \cdot 1

\frac{1}{6} \cdot 4 \cdot 1 = \frac{2}{3}

= \frac{2}{3}

3135825 (1 + \frac{1}{9050000 s})

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