What is log_{a}((x^4)/(y^2a^4)) ?

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

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simplify log_{a}((x^4)/(y^2a^4))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

lo g_{a} (x^{4}) = 4 lo g_{a} (x)

lo g_{a} (y^{2} a^{4}) = 2 lo g_{a} (y) + 4

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

Apply the distributive law:

- (a + b) = - a - b

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

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

2 lo g_{10} (x) - 2 lo g_{10} (x + 1)

ln (- 2 e^{- x})

- ln (\frac{1}{5})

lo g_{10} (a b^{6} \cdot c^{3})

lo g_{10} (\frac{x ^{2} + 1}{1000000})

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