What is log_{sqrt(8)}(\sqrt[3]{4}) ?

The solution to log_{sqrt(8)}(\sqrt[3]{4}) is 4/9

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simplify log_{sqrt(8)}(\sqrt[3]{4})

simplify

\frac{4}{9}

Decimal Notation

0.44444 \dots

Solution steps

Factor

8 : 2^{\frac{3}{2}}

Apply log rule:

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

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

Apply log rule:

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

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

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

\frac{1}{\frac{3}{2}} \cdot \frac{2}{3} = \frac{4}{9}

= \frac{4}{9}

18000

\frac{7}{8} \div \frac{5}{6}

\frac{8 w ^{2} - 20 w - 12}{2 w + 1}

r^{2} - 5 r - 24

What is log_{sqrt(8)}(\sqrt[3]{4}) ?
The solution to log_{sqrt(8)}(\sqrt[3]{4}) is 4/9