What is log_{a}((x^2)/(yz^3)) ?

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

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simplify log_{a}((x^2)/(yz^3))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

lo g_{a} (y z^{3}) = lo g_{a} (y) + 3 lo g_{a} (z)

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

Apply the distributive law:

- (a + b) = - a - b

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

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

\frac{1}{2} (lo g_{5} (x - 8) - lo g_{5} (x))

lo g_{4} (\frac{x ^{2}}{5})

lo g_{10} (1 x)

ln (x^{2} - 81) - ln (x^{2} - 6 x - 27)

lo g_{7} ((\frac{x}{y})^{2})

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