What is log_{x}((sqrt(x))/y) ?

The solution to log_{x}((sqrt(x))/y) is 1/2-log_{x}(y)

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simplify log_{x}((sqrt(x))/y)

simplify

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

\frac{1}{2} - lo g_{x} (y)

Solution steps

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

Apply log rule:

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

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

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

Simplify

lo g_{x} (x) : \frac{1}{2}

= \frac{1}{2} - lo g_{x} (y)

lo g_{10} (10 x) + lo g_{10} (10 y)

lo g_{10} (x) + 2 lo g_{10} (6 y)

- 0.1 lo g_{2} (0.1) - 0.9 lo g_{2} (0.9)

lo g_{10} (2) + lo g_{10} (x + 3) - lo g_{10} (x + 5)

ln (\frac{10}{x})

What is log_{x}((sqrt(x))/y) ?
The solution to log_{x}((sqrt(x))/y) is 1/2-log_{x}(y)