What is log_{10}(x^{3/5}y^4) ?

The solution to log_{10}(x^{3/5}y^4) is 3/5 log_{10}(x)+4log_{10}(y)

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simplify log_{10}(x^{3/5}y^4)

simplify

lo g_{10} (x^{\frac{3}{5}} y^{4})

\frac{3}{5} lo g_{10} (x) + 4 lo g_{10} (y)

Solution steps

lo g_{10} (x^{\frac{3}{5}} y^{4})

Apply log rule:

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

lo g_{10} (x^{\frac{3}{5}} y^{4}) = lo g_{10} (x^{\frac{3}{5}}) + lo g_{10} (y^{4})

= lo g_{10} (x^{\frac{3}{5}}) + lo g_{10} (y^{4})

lo g_{10} (x^{\frac{3}{5}}) = \frac{3}{5} lo g_{10} (x)

lo g_{10} (y^{4}) = 4 lo g_{10} (y)

= \frac{3}{5} lo g_{10} (x) + 4 lo g_{10} (y)

lo g_{10} (x^{3} \cdot y^{- 2})

ln (x + 3) - ln (2 x)

\frac{1}{3} lo g_{b} (x) + 5 lo g_{b} (y) - 4 lo g_{b} (x)

ln (\frac{( t + 5 ) ^{3}}{t ^{4} ( 5 - 1 ) ^{2}})

What is log_{10}(x^{3/5}y^4) ?
The solution to log_{10}(x^{3/5}y^4) is 3/5 log_{10}(x)+4log_{10}(y)