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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

89.9 (- ln ∣ 0.3 + 0.2 ∣ + ln ∣ 0.2 ∣)

\frac{18}{16 π ^{2}} ln (\frac{( 16 ) ^{2}}{0.03 \cdot 16 π ^{2}})

- 4 ln (5) + \frac{1}{3} ln (y)

lo g_{10} (\frac{x}{5})

ln (\frac{( x + 2 ) ^{6}}{x ^{5}})

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