What is 9log_{5}(x)+log_{5}(y) ?

The solution to 9log_{5}(x)+log_{5}(y) is log_{5}(x^9y)

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simplify 9log_{5}(x)+log_{5}(y)

simplify

9 lo g_{5} (x) + lo g_{5} (y)

lo g_{5} (x^{9} y)

Solution steps

9 lo g_{5} (x) + lo g_{5} (y)

Apply log rule:

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

9 lo g_{5} (x) = lo g_{5} (x^{9})

= lo g_{5} (x^{9}) + lo g_{5} (y)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{5} (x^{9}) + lo g_{5} (y) = lo g_{5} (x^{9} y)

= lo g_{5} (x^{9} y)

5 ln (3 x)

\frac{1}{2} lo g_{a} (- 3 lo g_{b} (x))

ln (e ln (x))

ln (4 x^{2}) + ln (3 x^{3})

lo g_{10} (\frac{10}{x}) - 2 - 2 lo g_{10} (x)

What is 9log_{5}(x)+log_{5}(y) ?
The solution to 9log_{5}(x)+log_{5}(y) is log_{5}(x^9y)