What is log_{a}((x^7)/(yz^8)) ?

The solution to log_{a}((x^7)/(yz^8)) is 7log_{a}(x)-log_{a}(y)-8log_{a}(z)

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simplify log_{a}((x^7)/(yz^8))

simplify

lo g_{a} (\frac{x ^{7}}{y z ^{8}})

7 lo g_{a} (x) - lo g_{a} (y) - 8 lo g_{a} (z)

Solution steps

lo g_{a} (\frac{x ^{7}}{y z ^{8}})

Apply log rule:

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

lo g_{a} (\frac{x ^{7}}{y z ^{8}}) = lo g_{a} (x^{7}) - lo g_{a} (y z^{8})

= lo g_{a} (x^{7}) - lo g_{a} (y z^{8})

lo g_{a} (x^{7}) = 7 lo g_{a} (x)

lo g_{a} (y z^{8}) = lo g_{a} (y) + 8 lo g_{a} (z)

= 7 lo g_{a} (x) - (lo g_{a} (y) + 8 lo g_{a} (z))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{a} (y) + 8 lo g_{a} (z)) = - lo g_{a} (y) - 8 lo g_{a} (z)

= 7 lo g_{a} (x) - lo g_{a} (y) - 8 lo g_{a} (z)

lo g_{7} ((5) (c))

lo g_{10} (3 x)

lo g_{5} (2 x) + lo g_{5} (x - 1)

lo g_{b} (\frac{9}{7})

\frac{15}{4} ln (\frac{5}{2})

What is log_{a}((x^7)/(yz^8)) ?
The solution to log_{a}((x^7)/(yz^8)) is 7log_{a}(x)-log_{a}(y)-8log_{a}(z)