What is log_{10}(\sqrt[3]{0.01sqrt(0.1)}) ?

The solution to log_{10}(\sqrt[3]{0.01sqrt(0.1)}) is -5/6

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simplify log_{10}(\sqrt[3]{0.01sqrt(0.1)})

simplify

lo g_{10} (3 0.01 0.1)

- \frac{5}{6}

Decimal

- 0.83333 \dots

Solution steps

lo g_{10} (3 0.01 0.1)

3 0.01 0.1 = 0.0 1^{\frac{1}{3}} \cdot 1 0^{- \frac{1}{6}}

= lo g_{10} (0.0 1^{\frac{1}{3}} \cdot 1 0^{- \frac{1}{6}})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{10} (0.0 1^{\frac{1}{3}} \cdot 1 0^{- \frac{1}{6}}) = lo g_{10} (0.0 1^{\frac{1}{3}}) + lo g_{10} (1 0^{- \frac{1}{6}})

= lo g_{10} (0.0 1^{\frac{1}{3}}) + lo g_{10} (1 0^{- \frac{1}{6}})

lo g_{10} (0.0 1^{\frac{1}{3}}) = - \frac{2}{3}

= - \frac{2}{3} + lo g_{10} (1 0^{- \frac{1}{6}})

Apply log rule:

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

lo g_{10} (1 0^{- \frac{1}{6}}) = - \frac{1}{6}

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

- \frac{2}{3} - \frac{1}{6} = - \frac{5}{6}

= - \frac{5}{6}

\frac{\frac{a - x}{a x}}{x - a}

(2 - 5 i) (- 2 + 7 i)

\frac{63}{36}

82 + 82

- 2 \times 3 x

What is log_{10}(\sqrt[3]{0.01sqrt(0.1)}) ?
The solution to log_{10}(\sqrt[3]{0.01sqrt(0.1)}) is -5/6