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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

2 lo g_{10} (y) = lo g_{10} (y^{2})

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

Apply log rule:

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

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

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

lo g_{6} (5 z)

lo g_{6} (5 x)

lo g_{8} (\frac{w ^{4} x ^{2}}{yz})

lo g_{10} (512) - lo g_{10} (366)

lo g_{10} (rs) - 3 lo g_{10} (p) + 7

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