What is log_{5}((x^2)/y) ?

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

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simplify log_{5}((x^2)/y)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

lo g_{5} (x^{2}) : 2 lo g_{5} (x)

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

4 lo g_{4} (x) + \frac{5}{3} lo g_{4} (y) - 6 lo g_{4} (z)

ln (- 2) - ln (- 6)

\frac{1}{3} ln (x) - \frac{1}{3} ln (y)

lo g_{5} (\frac{x ^{3} x ^{2} + 1}{( x + 1 ) ^{4}})

\frac{1}{2} lo g_{10} (x) + 3 lo g_{10} (y)

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