What is log_{10}(x)+1/5 log_{10}(y) ?

The solution to log_{10}(x)+1/5 log_{10}(y) is log_{10}(xy^{1/5})

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simplify log_{10}(x)+1/5 log_{10}(y)

simplify

lo g_{10} (x) + \frac{1}{5} lo g_{10} (y)

lo g_{10} (x y^{\frac{1}{5}})

Solution steps

lo g_{10} (x) + \frac{1}{5} lo g_{10} (y)

Apply log rule:

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

\frac{1}{5} lo g_{10} (y) = lo g_{10} (y^{\frac{1}{5}})

= lo g_{10} (x) + lo g_{10} (y^{\frac{1}{5}})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{10} (x) + lo g_{10} (y^{\frac{1}{5}}) = lo g_{10} (x y^{\frac{1}{5}})

= lo g_{10} (x y^{\frac{1}{5}})

(75.3) ln (\frac{100}{30})

lo g_{4} (\frac{x ^{3} e ^{2}}{( 4 x + 1 ) ^{\frac{1}{2}}})

ln (x - 9) + ln (x + 9)

\frac{1}{2} ln (\frac{78}{118})

ln (5 \cdot e^{x})

What is log_{10}(x)+1/5 log_{10}(y) ?
The solution to log_{10}(x)+1/5 log_{10}(y) is log_{10}(xy^{1/5})