What is log_{10}(0.485^{1/4}*0.36^{1/3}) ?

The solution to log_{10}(0.485^{1/4}*0.36^{1/3}) is 1/4 log_{10}(485)-17/12+2/3 log_{10}(6)

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simplify log_{10}(0.485^{1/4}*0.36^{1/3})

simplify

lo g_{10} (0.48 5^{\frac{1}{4}} \cdot 0.3 6^{\frac{1}{3}})

\frac{1}{4} lo g_{10} (485) - \frac{17}{12} + \frac{2}{3} lo g_{10} (6)

Decimal Notation

- 0.22646 \dots

Solution steps

lo g_{10} (0.48 5^{\frac{1}{4}} \cdot 0.3 6^{\frac{1}{3}})

Apply log rule:

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

lo g_{10} (0.48 5^{\frac{1}{4}} \cdot 0.3 6^{\frac{1}{3}}) = lo g_{10} (0.48 5^{\frac{1}{4}}) + lo g_{10} (0.3 6^{\frac{1}{3}})

= lo g_{10} (0.48 5^{\frac{1}{4}}) + lo g_{10} (0.3 6^{\frac{1}{3}})

lo g_{10} (0.48 5^{\frac{1}{4}}) = \frac{1}{4} lo g_{10} (485) - \frac{3}{4}

lo g_{10} (0.3 6^{\frac{1}{3}}) = \frac{2}{3} lo g_{10} (6) - \frac{2}{3}

= \frac{1}{4} lo g_{10} (485) - \frac{3}{4} + \frac{2}{3} lo g_{10} (6) - \frac{2}{3}

\frac{1}{4} lo g_{10} (485) - \frac{3}{4} + \frac{2}{3} lo g_{10} (6) - \frac{2}{3} = \frac{1}{4} lo g_{10} (485) - \frac{17}{12} + \frac{2}{3} lo g_{10} (6)

= \frac{1}{4} lo g_{10} (485) - \frac{17}{12} + \frac{2}{3} lo g_{10} (6)

ln (3 x) - 2 ln (x)

ln (a) + ln (\frac{1}{2 b}) - b (\frac{1}{2 b})^{2}

e lo g_{3} (\frac{1}{81}) + lo g_{\frac{1}{3}} (\frac{1}{61})_{e}

ln (\frac{4}{e})

ln (\frac{1}{θ + a})

What is log_{10}(0.485^{1/4}*0.36^{1/3}) ?
The solution to log_{10}(0.485^{1/4}*0.36^{1/3}) is 1/4 log_{10}(485)-17/12+2/3 log_{10}(6)