What is log_{3}((sqrt(3x^5))/y) ?

The solution to log_{3}((sqrt(3x^5))/y) is (1+5log_{3}(x))/2-log_{3}(y)

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simplify log_{3}((sqrt(3x^5))/y)

simplify

lo g_{3} (\frac{3 x ^{5}}{y})

\frac{1 + 5 lo g _{3} ( x )}{2} - lo g_{3} (y)

Solution steps

lo g_{3} (\frac{3 x ^{5}}{y})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{3} (\frac{3 x ^{5}}{y}) = lo g_{3} (3 x^{5}) - lo g_{3} (y)

= lo g_{3} (3 x^{5}) - lo g_{3} (y)

Simplify

lo g_{3} (3 x^{5}) : \frac{1 + 5 lo g _{3} ( x )}{2}

= \frac{1 + 5 lo g _{3} ( x )}{2} - lo g_{3} (y)

ln (a + b) + ln (a - b) - 6 ln (c)

lo g_{10} (2) + lo g_{10} (3) + lo g_{10} (4)

\frac{2}{3} ln (x) - \frac{1}{2} ln (y)

ln (\frac{1}{x ^{n}})

lo g_{3} (6) - lo g_{3} (4)

What is log_{3}((sqrt(3x^5))/y) ?
The solution to log_{3}((sqrt(3x^5))/y) is (1+5log_{3}(x))/2-log_{3}(y)