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Popular >

simplify log_{\sqrt[3]{2}}(32)

Solution

simplify

Solution

15

Solution steps

Apply radical rule:

= lo g_{2^{\frac{1}{3}}} (32)

Apply log rule:

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

lo g_{2^{\frac{1}{3}}} (32) = \frac{1}{\frac{1}{3}} lo g_{2} (32)

= \frac{1}{\frac{1}{3}} lo g_{2} (32)

Factor the number:

32 = 2^{5}

= \frac{1}{\frac{1}{3}} lo g_{2} (2^{5})

Apply log rule:

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

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

= \frac{1}{\frac{1}{3}} \cdot 5

\frac{1}{\frac{1}{3}} \cdot 5 = 15

= 15

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Frequently Asked Questions (FAQ)

What is log_{\sqrt[3]{2}}(32) ?
The solution to log_{\sqrt[3]{2}}(32) is 15