What is log_{a}((x^4)/(yz^5)) ?

The solution to log_{a}((x^4)/(yz^5)) is 4log_{a}(x)-log_{a}(y)-5log_{a}(z)

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simplify log_{a}((x^4)/(yz^5))

simplify

lo g_{a} (\frac{x ^{4}}{y z ^{5}})

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

Solution steps

lo g_{a} (\frac{x ^{4}}{y z ^{5}})

Apply log rule:

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

lo g_{a} (\frac{x ^{4}}{y z ^{5}}) = lo g_{a} (x^{4}) - lo g_{a} (y z^{5})

= lo g_{a} (x^{4}) - lo g_{a} (y z^{5})

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

lo g_{a} (y z^{5}) = lo g_{a} (y) + 5 lo g_{a} (z)

= 4 lo g_{a} (x) - (lo g_{a} (y) + 5 lo g_{a} (z))

Apply the distributive law:

- (a + b) = - a - b

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

= 4 lo g_{a} (x) - lo g_{a} (y) - 5 lo g_{a} (z)

lo g_{14} (14 x)

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

ln (x) - ln (x + 2) + ln (2 x - 3)

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

ln (x^{2} \frac{y}{z})

What is log_{a}((x^4)/(yz^5)) ?
The solution to log_{a}((x^4)/(yz^5)) is 4log_{a}(x)-log_{a}(y)-5log_{a}(z)