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Popular >

simplify log_{1/8}(4)

Solution

simplify

lo g_{\frac{1}{8}} (4)

Solution

- \frac{2}{3}

+1

Decimal Notation

- 0.66666 \dots

Solution steps

lo g_{\frac{1}{8}} (4)

Apply log rule:

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

lo g_{\frac{1}{8}} (4) = - lo g_{8} (4)

= - lo g_{8} (4)

Factor the number:

8 = 2^{3}

= - lo g_{2^{3}} (4)

Apply log rule:

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

lo g_{2^{3}} (4) = \frac{1}{3} lo g_{2} (4)

= - \frac{1}{3} lo g_{2} (4)

Factor the number:

4 = 2^{2}

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

Apply log rule:

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

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

= - \frac{1}{3} \cdot 2

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

= - \frac{2}{3}

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Frequently Asked Questions (FAQ)

What is log_{1/8}(4) ?
The solution to log_{1/8}(4) is -2/3