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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

\frac{\frac{a}{x}}{a x} : \frac{a}{x}

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

lo g_{7} (49) = y

x^{2} - 14 x + 19 = 0

x^{2} + 14 x + 45

- 4 x^{2} - 16 x + 180

\frac{7}{16} + \frac{3}{8}

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