What is expand log_{3}((x^6)/(5y)) ?

The solution to expand log_{3}((x^6)/(5y)) is 6log_{3}(x)-log_{3}(5)-log_{3}(y)

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expand log_{3}((x^6)/(5y))

expand

lo g_{3} (\frac{x ^{6}}{5 y})

6 lo g_{3} (x) - lo g_{3} (5) - lo g_{3} (y)

Solution steps

lo g_{3} (\frac{x ^{6}}{5 y})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{3} (\frac{x ^{6}}{5 y}) = lo g_{3} (x^{6}) - lo g_{3} (5 y)

= lo g_{3} (x^{6}) - lo g_{3} (5 y)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{3} (x^{6}) = 6 lo g_{3} (x)

= 6 lo g_{3} (x) - lo g_{3} (5 y)

Apply log rule:

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

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

= 6 lo g_{3} (x) - (lo g_{3} (y) + lo g_{3} (5))

- (lo g_{3} (5) + lo g_{3} (y)) : - lo g_{3} (5) - lo g_{3} (y)

= 6 lo g_{3} (x) - lo g_{3} (5) - lo g_{3} (y)

20 lo g_{10} (\frac{2.5 \cdot 1 0 ^{- 3}}{2}) + 4

- ln (x) + 9 ln (y) - 3 ln (z)

ln (\frac{n + 1}{n - 1})

ln (\frac{x}{e ^{x} ( x + 3 ) ^{2}})

ln (\frac{x ^{9} x ^{2} + 2}{( x + 2 ) ^{5}})

What is expand log_{3}((x^6)/(5y)) ?
The solution to expand log_{3}((x^6)/(5y)) is 6log_{3}(x)-log_{3}(5)-log_{3}(y)