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Popular >

simplify log_{49}(\sqrt[3]{7})

Solution

simplify

Solution

\frac{1}{6}

+1

Decimal Notation

0.16666 \dots

Solution steps

Factor the number:

49 = 7^{2}

Apply log rule:

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

Apply radical rule:

= \frac{1}{2} lo g_{7} (7^{\frac{1}{3}})

Apply log rule:

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

lo g_{7} (7^{\frac{1}{3}}) = \frac{1}{3}

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

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

= \frac{1}{6}

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Frequently Asked Questions (FAQ)

What is log_{49}(\sqrt[3]{7}) ?
The solution to log_{49}(\sqrt[3]{7}) is 1/6