What is 5log_{a}(x)-2log_{a}(y) ?

The solution to 5log_{a}(x)-2log_{a}(y) is log_{a}((x^5)/(y^2))

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simplify 5log_{a}(x)-2log_{a}(y)

simplify

5 lo g_{a} (x) - 2 lo g_{a} (y)

lo g_{a} (\frac{x ^{5}}{y ^{2}})

Solution steps

5 lo g_{a} (x) - 2 lo g_{a} (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

5 lo g_{a} (x) = lo g_{a} (x^{5})

= lo g_{a} (x^{5}) - 2 lo g_{a} (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= lo g_{a} (x^{5}) - lo g_{a} (y^{2})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{a} (x^{5}) - lo g_{a} (y^{2}) = lo g_{a} (\frac{x ^{5}}{y ^{2}})

= lo g_{a} (\frac{x ^{5}}{y ^{2}})

ln (3 ln (2))

\frac{ln ( 807 ) - ln ( 40.2 )}{2 - 1}

ln (\frac{x + 2}{x})

ln (\frac{0.19556}{0.1924})

\frac{ln ( 40 ) - ln ( 7 )}{3 ln ( 7 )}

What is 5log_{a}(x)-2log_{a}(y) ?
The solution to 5log_{a}(x)-2log_{a}(y) is log_{a}((x^5)/(y^2))