What is expand log_{3}((9x)/(y^2)) ?

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

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expand log_{3}((9x)/(y^2))

expand

lo g_{3} (\frac{9 x}{y ^{2}})

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

Solution steps

lo g_{3} (\frac{9 x}{y ^{2}})

Apply log rule:

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

lo g_{3} (\frac{9 x}{y ^{2}}) = lo g_{3} (9 x) - lo g_{3} (y^{2})

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

Apply log rule:

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

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

= lo g_{3} (9 x) - 2 lo g_{3} (y)

Apply log rule:

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

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

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

lo g_{3} (9) = 2

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

20 lo g_{10} (\frac{p}{2 x 1 0 ^{- 5}})

lo g_{3} (x) + 2 lo g_{3} (y) + \frac{1}{2} lo g_{3} (z)

2 lo g_{b} (x) + 4 lo g_{b} (y) - 3 lo g_{b} (z)

ln (\frac{a ^{- 2} b ^{3}}{c ^{- 5}})

ln (x^{12} 2 - x)

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