What is log_{10}((sqrt(0.35))/(\sqrt[3]{0.85)}) ?

The solution to log_{10}((sqrt(0.35))/(\sqrt[3]{0.85)}) is 1/2 log_{10}(0.35)-1/3 log_{10}(0.85)

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simplify log_{10}((sqrt(0.35))/(\sqrt[3]{0.85)})

simplify

\frac{1}{2} lo g_{10} (0.35) - \frac{1}{3} lo g_{10} (0.85)

Decimal Notation

- 0.20443 \dots

Solution steps

Apply log rule:

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

lo g_{10} (0.35) = \frac{1}{2} lo g_{10} (0.35)

= \frac{1}{2} lo g_{10} (0.35) - \frac{1}{3} lo g_{10} (0.85)

5 ln (\frac{9}{8}) + 1.5 ln (\frac{13}{9}) + 3 ln (\frac{14}{13})

(ln (c (t)) - ln (c)) e^{r t}

lo g_{e} (x^{4} - 16) - 3 lo g_{e} (x - 2)

ln (5 \cdot 1 0^{12 - 4})

What is log_{10}((sqrt(0.35))/(\sqrt[3]{0.85)}) ?
The solution to log_{10}((sqrt(0.35))/(\sqrt[3]{0.85)}) is 1/2 log_{10}(0.35)-1/3 log_{10}(0.85)