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Popular >

simplify log_{1/4}(32)

Solution

simplify

lo g_{\frac{1}{4}} (32)

Solution

- \frac{5}{2}

+1

Decimal Notation

- 2.5

Solution steps

lo g_{\frac{1}{4}} (32)

Apply log rule:

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

= - lo g_{4} (32)

Rewrite

4

as

2^{2}

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

Apply log rule:

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

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

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

Rewrite

32

in power-base form:

32 = 2^{5}

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (a) = 1

lo g_{2} (2) = 1

= - \frac{1}{2} \cdot 5 \cdot 1

- \frac{1}{2} \cdot 5 \cdot 1 = - \frac{5}{2}

= - \frac{5}{2}

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Frequently Asked Questions (FAQ)

What is log_{1/4}(32) ?
The solution to log_{1/4}(32) is -5/2