What is log_{a}((x^2y)/(sqrt(z))) ?

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

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simplify log_{a}((x^2y)/(sqrt(z)))

simplify

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

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

Solution steps

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

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

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

Simplify

lo g_{a} (x^{2} y) : 2 lo g_{a} (x) + lo g_{a} (y)

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

ln (10 e)

lo g_{10} (\frac{7 z}{9})

lo g_{7} (7 m n^{4})

\frac{ln ( 2 )}{ln ( 3 ) - ln ( 2 )}

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