What is 1/3 log_{4}(x)+log_{4}(y)-2 ?

The solution to 1/3 log_{4}(x)+log_{4}(y)-2 is log_{4}(x^{1/3}y)-2

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simplify 1/3 log_{4}(x)+log_{4}(y)-2

simplify

\frac{1}{3} lo g_{4} (x) + lo g_{4} (y) - 2

lo g_{4} (x^{\frac{1}{3}} y) - 2

Solution steps

\frac{1}{3} lo g_{4} (x) + lo g_{4} (y) - 2

Apply log rule:

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

\frac{1}{3} lo g_{4} (x) = lo g_{4} (x^{\frac{1}{3}})

= lo g_{4} (x^{\frac{1}{3}}) + lo g_{4} (y) - 2

Apply log rule:

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

lo g_{4} (x^{\frac{1}{3}}) + lo g_{4} (y) = lo g_{4} (y x^{\frac{1}{3}})

= lo g_{4} (x^{\frac{1}{3}} y) - 2

2 lo g_{10} (2 x)

ln (x yz)

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

lo g_{4} (\frac{g}{64})

ln (- 3) - ln (- 1)

What is 1/3 log_{4}(x)+log_{4}(y)-2 ?
The solution to 1/3 log_{4}(x)+log_{4}(y)-2 is log_{4}(x^{1/3}y)-2