What is 3log_{5}(x)-log_{5}(y) ?

The solution to 3log_{5}(x)-log_{5}(y) is log_{5}((x^3)/y)

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simplify 3log_{5}(x)-log_{5}(y)

simplify

3 lo g_{5} (x) - lo g_{5} (y)

lo g_{5} (\frac{x ^{3}}{y})

Solution steps

3 lo g_{5} (x) - lo g_{5} (y)

Apply log rule:

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

3 lo g_{5} (x) = lo g_{5} (x^{3})

= lo g_{5} (x^{3}) - lo g_{5} (y)

Apply log rule:

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

lo g_{5} (x^{3}) - lo g_{5} (y) = lo g_{5} (\frac{x ^{3}}{y})

= lo g_{5} (\frac{x ^{3}}{y})

\frac{1}{3} [2 ln (x + 3) + ln (x) - ln (x^{2} - 1)]

lo g_{10} (3) + lo g_{10} (2)

lo g_{10} (12) + \frac{1}{2} lo g_{10} (7) - lo g_{10} (2)

lo g_{10} (3) + lo g_{10} (4)

lo g_{10} (\frac{6 ( x + 4 ) ^{3}}{x ^{5}})

What is 3log_{5}(x)-log_{5}(y) ?
The solution to 3log_{5}(x)-log_{5}(y) is log_{5}((x^3)/y)