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

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

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

simplify

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

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

Solution steps

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

Rewrite as

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

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

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

Simplify

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

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

5 (2 x + 3)

- 5.1 - 65

(2 x - 3) (3 x - 4)

\frac{3}{5} + \frac{2}{5}

\frac{50}{10}

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