What is log_{a}(sqrt(x))-log_{a}(1/x) ?

The solution to log_{a}(sqrt(x))-log_{a}(1/x) is log_{a}(sqrt(x)x)

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simplify log_{a}(sqrt(x))-log_{a}(1/x)

simplify

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

lo g_{a} (x x)

Solution steps

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

Apply log rule:

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

lo g_{a} (x) - lo g_{a} (\frac{1}{x}) = lo g_{a} (\frac{x}{\frac{1}{x}})

= lo g_{a} (\frac{x}{\frac{1}{x}})

Simplify

\frac{x}{\frac{1}{x}} : x x

= lo g_{a} (x x)

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

e^{x} - ln (4 e^{e^{x}})

ln (10) - ln (5)

lo g_{b} (\frac{x ^{2} y}{z ^{6}})

lo g_{10} (\frac{y ^{7}}{x z ^{3}})

What is log_{a}(sqrt(x))-log_{a}(1/x) ?
The solution to log_{a}(sqrt(x))-log_{a}(1/x) is log_{a}(sqrt(x)x)