What is log_{a}((x^5)/(yz^6)) ?

The solution to log_{a}((x^5)/(yz^6)) is 5log_{a}(x)-log_{a}(y)-6log_{a}(z)

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simplify log_{a}((x^5)/(yz^6))

simplify

lo g_{a} (\frac{x ^{5}}{y z ^{6}})

5 lo g_{a} (x) - lo g_{a} (y) - 6 lo g_{a} (z)

Solution steps

lo g_{a} (\frac{x ^{5}}{y z ^{6}})

Apply log rule:

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

lo g_{a} (\frac{x ^{5}}{y z ^{6}}) = lo g_{a} (x^{5}) - lo g_{a} (y z^{6})

= lo g_{a} (x^{5}) - lo g_{a} (y z^{6})

lo g_{a} (x^{5}) = 5 lo g_{a} (x)

lo g_{a} (y z^{6}) = lo g_{a} (y) + 6 lo g_{a} (z)

= 5 lo g_{a} (x) - (lo g_{a} (y) + 6 lo g_{a} (z))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{a} (y) + 6 lo g_{a} (z)) = - lo g_{a} (y) - 6 lo g_{a} (z)

= 5 lo g_{a} (x) - lo g_{a} (y) - 6 lo g_{a} (z)

5 lo g_{93} (3)

2 ln (x) - \frac{3}{2} ln (y) + \frac{1}{2} ln (z)

\frac{1}{2} ln (x) + 6 ln (y) - 7 ln (z)

- (ln (3 x))^{2} + 10 ln (3 x)

What is log_{a}((x^5)/(yz^6)) ?
The solution to log_{a}((x^5)/(yz^6)) is 5log_{a}(x)-log_{a}(y)-6log_{a}(z)