What is log_{a}((x^2)/(yz^7)) ?

The solution to log_{a}((x^2)/(yz^7)) is 2log_{a}(x)-log_{a}(y)-7log_{a}(z)

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simplify log_{a}((x^2)/(yz^7))

simplify

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

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

Solution steps

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

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 ^{7}}) = lo g_{a} (x^{2}) - lo g_{a} (y z^{7})

= lo g_{a} (x^{2}) - lo g_{a} (y z^{7})

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

lo g_{a} (y z^{7}) = lo g_{a} (y) + 7 lo g_{a} (z)

= 2 lo g_{a} (x) - (lo g_{a} (y) + 7 lo g_{a} (z))

Apply the distributive law:

- (a + b) = - a - b

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

= 2 lo g_{a} (x) - lo g_{a} (y) - 7 lo g_{a} (z)

lo g_{10} (6) + 4 lo g_{10} (x)

\frac{1}{2} lo g_{3} (10)

lo g_{5} (25 x^{2})

ln (4) + ln (x) - 3 ln (2)

lo g_{10} (x) + lo g_{10} (x + 9)

What is log_{a}((x^2)/(yz^7)) ?
The solution to log_{a}((x^2)/(yz^7)) is 2log_{a}(x)-log_{a}(y)-7log_{a}(z)