What is log_{5}(sqrt(x))-log_{5}(x^2) ?

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

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simplify log_{5}(sqrt(x))-log_{5}(x^2)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

ln (22)

ln (x^{2} - 81) - ln (x + 9)

lo g_{10} (\frac{y ^{5} x}{z})

2 lo g_{10} (x) - 4 lo g_{10} (x + 5) + \frac{1}{x} lo g_{10} (3 x + 5)

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