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

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

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expand log_{3}((x^2)/y)

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

x - \frac{1}{2} lo g_{15} (17) + \frac{1}{2} lo g_{15} (3)

lo g_{9} (\frac{x ( x ^{2} + 7 )}{x ^{2} - 7})

9 lo g_{22} (2)

- lo g_{10} (3.2 e^{- 4})

lo g_{e} ((\frac{y - 1}{3})^{2})

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