What is 1/2 log_{7}(x)+1/3 log_{7}(y) ?

The solution to 1/2 log_{7}(x)+1/3 log_{7}(y) is log_{7}(x^{1/2}y^{1/3})

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simplify 1/2 log_{7}(x)+1/3 log_{7}(y)

simplify

\frac{1}{2} lo g_{7} (x) + \frac{1}{3} lo g_{7} (y)

lo g_{7} (x^{\frac{1}{2}} y^{\frac{1}{3}})

Solution steps

\frac{1}{2} lo g_{7} (x) + \frac{1}{3} lo g_{7} (y)

Apply log rule:

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

\frac{1}{2} lo g_{7} (x) = lo g_{7} (x^{\frac{1}{2}})

= lo g_{7} (x^{\frac{1}{2}}) + \frac{1}{3} lo g_{7} (y)

Apply log rule:

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

\frac{1}{3} lo g_{7} (y) = lo g_{7} (y^{\frac{1}{3}})

= lo g_{7} (x^{\frac{1}{2}}) + lo g_{7} (y^{\frac{1}{3}})

Apply log rule:

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

lo g_{7} (x^{\frac{1}{2}}) + lo g_{7} (y^{\frac{1}{3}}) = lo g_{7} (x^{\frac{1}{2}} y^{\frac{1}{3}})

= lo g_{7} (x^{\frac{1}{2}} y^{\frac{1}{3}})

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- lo g_{10} (1.2 \cdot 1 0^{- 3})

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

What is 1/2 log_{7}(x)+1/3 log_{7}(y) ?
The solution to 1/2 log_{7}(x)+1/3 log_{7}(y) is log_{7}(x^{1/2}y^{1/3})