What is log_{3}((81x^2)/(ysqrt(z))) ?

The solution to log_{3}((81x^2)/(ysqrt(z))) is 4+2log_{3}(x)-log_{3}(y)-log_{3}(sqrt(z))

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simplify log_{3}((81x^2)/(ysqrt(z)))

simplify

lo g_{3} (\frac{81 x ^{2}}{y z})

4 + 2 lo g_{3} (x) - lo g_{3} (y) - lo g_{3} (z)

Solution steps

lo g_{3} (\frac{81 x ^{2}}{y z})

Apply log rule:

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

lo g_{3} (\frac{81 x ^{2}}{y z}) = lo g_{3} (81 x^{2}) - lo g_{3} (y z)

= lo g_{3} (81 x^{2}) - lo g_{3} (y z)

lo g_{3} (81 x^{2}) = 4 + 2 lo g_{3} (x)

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

= 4 + 2 lo g_{3} (x) - (lo g_{3} (y) + lo g_{3} (z))

Apply the distributive law:

- (a + b) = - a - b

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

= 4 + 2 lo g_{3} (x) - lo g_{3} (y) - lo g_{3} (z)

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What is log_{3}((81x^2)/(ysqrt(z))) ?
The solution to log_{3}((81x^2)/(ysqrt(z))) is 4+2log_{3}(x)-log_{3}(y)-log_{3}(sqrt(z))