What is log_{3}((9sqrt(x^7))/(y^5)) ?

The solution to log_{3}((9sqrt(x^7))/(y^5)) is 2+3log_{3}(x)+log_{3}(sqrt(x))-5log_{3}(y)

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simplify log_{3}((9sqrt(x^7))/(y^5))

simplify

lo g_{3} (\frac{9 x ^{7}}{y ^{5}})

2 + 3 lo g_{3} (x) + lo g_{3} (x) - 5 lo g_{3} (y)

Solution steps

lo g_{3} (\frac{9 x ^{7}}{y ^{5}})

Simplify

x^{7} : x^{3} x

= lo g_{3} (\frac{9 x ^{3} x}{y ^{5}})

Apply log rule:

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

lo g_{3} (\frac{9 x ^{3} x}{y ^{5}}) = lo g_{3} (9 x^{3} x) - lo g_{3} (y^{5})

= lo g_{3} (9 x^{3} x) - lo g_{3} (y^{5})

lo g_{3} (9 x^{3} x) = 2 + 3 lo g_{3} (x) + lo g_{3} (x)

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

= 2 + 3 lo g_{3} (x) + lo g_{3} (x) - 5 lo g_{3} (y)

lo g_{3} (9 v)

lo g_{a} (a^{2} x) - lo g_{a} (x^{2} a)

- 3 (ln (3) - ln (2))

lo g_{7} (\frac{x ^{3}}{y ^{4}})

What is log_{3}((9sqrt(x^7))/(y^5)) ?
The solution to log_{3}((9sqrt(x^7))/(y^5)) is 2+3log_{3}(x)+log_{3}(sqrt(x))-5log_{3}(y)