What is log_{a}((x^3)/(yz^4)) ?

The solution to log_{a}((x^3)/(yz^4)) is 3log_{a}(x)-log_{a}(y)-4log_{a}(z)

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simplify log_{a}((x^3)/(yz^4))

simplify

lo g_{a} (\frac{x ^{3}}{y z ^{4}})

3 lo g_{a} (x) - lo g_{a} (y) - 4 lo g_{a} (z)

Solution steps

lo g_{a} (\frac{x ^{3}}{y z ^{4}})

Apply log rule:

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

lo g_{a} (\frac{x ^{3}}{y z ^{4}}) = lo g_{a} (x^{3}) - lo g_{a} (y z^{4})

= lo g_{a} (x^{3}) - lo g_{a} (y z^{4})

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

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

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

Apply the distributive law:

- (a + b) = - a - b

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

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

ln (\frac{1}{2 π})

lo g_{10} (\frac{1}{x y})

lo g_{b} (x^{2} z)

2 lo g_{10} (3 w) - lo g_{10} (w + 4)

ln (\frac{x ^{2} - 1}{x ^{5}})

What is log_{a}((x^3)/(yz^4)) ?
The solution to log_{a}((x^3)/(yz^4)) is 3log_{a}(x)-log_{a}(y)-4log_{a}(z)