What is log_{10}((\sqrt[3]{0.02})/(sqrt(8))) ?

The solution to log_{10}((\sqrt[3]{0.02})/(sqrt(8))) is 1/3 log_{10}(0.02)-3/2 log_{10}(2)

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simplify log_{10}((\sqrt[3]{0.02})/(sqrt(8)))

simplify

\frac{1}{3} lo g_{10} (0.02) - \frac{3}{2} lo g_{10} (2)

Decimal Notation

- 1.01786 \dots

Solution steps

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (8) = \frac{1}{2} lo g_{10} (8)

= \frac{1}{3} lo g_{10} (0.02) - \frac{1}{2} lo g_{10} (8)

\frac{1}{2} lo g_{10} (8) = \frac{3}{2} lo g_{10} (2)

= \frac{1}{3} lo g_{10} (0.02) - \frac{3}{2} lo g_{10} (2)

4.89 + lo g_{10} (\frac{0.35}{0.15})

- 20 lo g_{10} (0.1) + 20 lo g_{10} (3)

10 \cdot lo g_{10} (\frac{x ^{7}}{lo g _{10} ( 1 0 ^{- 12} )})

ln (\frac{3}{23}) + (\frac{2}{23}) ln (23)

ln (178) - ln (713)

What is log_{10}((\sqrt[3]{0.02})/(sqrt(8))) ?
The solution to log_{10}((\sqrt[3]{0.02})/(sqrt(8))) is 1/3 log_{10}(0.02)-3/2 log_{10}(2)