What is log_{a}(a^2sqrt(x))-log_{a}(x^2sqrt(a)) ?

The solution to log_{a}(a^2sqrt(x))-log_{a}(x^2sqrt(a)) is log_{a}((asqrt(a))/(xsqrt(x)))

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simplify log_{a}(a^2sqrt(x))-log_{a}(x^2sqrt(a))

simplify

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

lo g_{a} (\frac{a a}{x x})

Solution steps

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

Apply log rule:

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

lo g_{a} (a^{2} x) - lo g_{a} (x^{2} a) = lo g_{a} (\frac{a ^{2} x}{x ^{2} a})

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

Cancel

\frac{a ^{2} x}{x ^{2} a} : \frac{a a}{x x}

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

- 3 (ln (3) - ln (2))

lo g_{7} (\frac{x ^{3}}{y ^{4}})

ln (\frac{a b ^{3}}{c d ^{3}})

lo g_{0.4} (\frac{3}{2}) - lo g_{2.5} (2)

What is log_{a}(a^2sqrt(x))-log_{a}(x^2sqrt(a)) ?
The solution to log_{a}(a^2sqrt(x))-log_{a}(x^2sqrt(a)) is log_{a}((asqrt(a))/(xsqrt(x)))