What is 3log_{4}(x)+log_{4}(y) ?

The solution to 3log_{4}(x)+log_{4}(y) is log_{4}(x^3y)

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simplify 3log_{4}(x)+log_{4}(y)

simplify

3 lo g_{4} (x) + lo g_{4} (y)

lo g_{4} (x^{3} y)

Solution steps

3 lo g_{4} (x) + lo g_{4} (y)

Apply log rule:

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

3 lo g_{4} (x) = lo g_{4} (x^{3})

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

Apply log rule:

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

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

= lo g_{4} (x^{3} y)

\frac{1}{3} ln (6) - \frac{1}{3} ln (3)

ln (\frac{901.8 + 150}{1907.2 + 150})

- lo g_{10} (4.07 \cdot 1 0^{- 5})

3 ln (x y) + ln (y) - ln (x^{3} y)

\frac{1}{3} ln (x) + \frac{10}{12} (x + 3) - \frac{1}{6} ln (x - 3)

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