What is 2/3*log_{10}(x)+1/3*log_{10}(y) ?

The solution to 2/3*log_{10}(x)+1/3*log_{10}(y) is log_{10}(x^{2/3}y^{1/3})

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simplify 2/3log_{10}(x)+1/3log_{10}(y)

simplify

\frac{2}{3} \cdot lo g_{10} (x) + \frac{1}{3} \cdot lo g_{10} (y)

lo g_{10} (x^{\frac{2}{3}} y^{\frac{1}{3}})

Solution steps

\frac{2}{3} lo g_{10} (x) + \frac{1}{3} lo g_{10} (y)

Apply log rule:

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

\frac{2}{3} lo g_{10} (x) = lo g_{10} (x^{\frac{2}{3}})

= lo g_{10} (x^{\frac{2}{3}}) + \frac{1}{3} lo g_{10} (y)

Apply log rule:

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

\frac{1}{3} lo g_{10} (y) = lo g_{10} (y^{\frac{1}{3}})

= lo g_{10} (x^{\frac{2}{3}}) + lo g_{10} (y^{\frac{1}{3}})

Apply log rule:

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

lo g_{10} (x^{\frac{2}{3}}) + lo g_{10} (y^{\frac{1}{3}}) = lo g_{10} (x^{\frac{2}{3}} y^{\frac{1}{3}})

= lo g_{10} (x^{\frac{2}{3}} y^{\frac{1}{3}})

\frac{1}{2} ln (\frac{c}{b ^{4} a})

ln (x + 1) - ln (x + 2)

lo g_{10} (x^{7})

e^{- 5 x} + 8 ln (2 z^{4})

ln (x^{n})

What is 2/3*log_{10}(x)+1/3*log_{10}(y) ?
The solution to 2/3*log_{10}(x)+1/3*log_{10}(y) is log_{10}(x^{2/3}y^{1/3})