What is expand log_{3}((x^2)/(81y^4)) ?

The solution to expand log_{3}((x^2)/(81y^4)) is 2log_{3}(x)-4-4log_{3}(y)

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expand log_{3}((x^2)/(81y^4))

expand

lo g_{3} (\frac{x ^{2}}{81 y ^{4}})

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

Solution steps

lo g_{3} (\frac{x ^{2}}{81 y ^{4}})

Apply log rule:

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

lo g_{3} (\frac{x ^{2}}{81 y ^{4}}) = lo g_{3} (x^{2}) - lo g_{3} (81 y^{4})

= lo g_{3} (x^{2}) - lo g_{3} (81 y^{4})

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} (81 y^{4})

Apply log rule:

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

lo g_{3} (81 y^{4}) = lo g_{3} (81) + lo g_{3} (y^{4})

= 2 lo g_{3} (x) - (lo g_{3} (y^{4}) + lo g_{3} (81))

Apply log rule:

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

lo g_{3} (y^{4}) = 4 lo g_{3} (y)

= 2 lo g_{3} (x) - (lo g_{3} (81) + 4 lo g_{3} (y))

lo g_{3} (81) = 4

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

- (4 + 4 lo g_{3} (y)) : - 4 - 4 lo g_{3} (y)

= 2 lo g_{3} (x) - 4 - 4 lo g_{3} (y)

\frac{5}{6} ln (\frac{40}{27})

lo g_{10} (x^{2} - 64) - 2 lo g_{10} (x - 8)

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

lo g_{b} (x^{6} z)

ln (2) + 2 ln (3)

What is expand log_{3}((x^2)/(81y^4)) ?
The solution to expand log_{3}((x^2)/(81y^4)) is 2log_{3}(x)-4-4log_{3}(y)