What is (1/(2sqrt(x)))^2+ln(1/(2sqrt(x))) ?

The solution to (1/(2sqrt(x)))^2+ln(1/(2sqrt(x))) is (1/(2sqrt(x)))^2++ln(1)-(ln(2)+ln(sqrt(x)))

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simplify (1/(2sqrt(x)))^2+ln(1/(2sqrt(x)))

simplify

(\frac{1}{2 x})^{2} + ln (\frac{1}{2 x})

(\frac{1}{2 x})^{2} + + ln (1) - (ln (2) + ln (x))

Solution steps

(\frac{1}{2 x})^{2} + ln (\frac{1}{2 x})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{1}{2 x}) = ln (1) - ln (2 x)

= (\frac{1}{2 x})^{2} + + ln (1) - ln (2 x)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (2 x) = ln (2) + ln (x)

= (\frac{1}{2 x})^{2} + + ln (1) - (ln (x) + ln (2))

lo g_{e} (\frac{2117}{1000})

- \frac{1}{2} ln (5)

ln (\frac{x}{100})

lo g_{4} (z x \cdot y)

3 ln (2) + ln (x)

What is (1/(2sqrt(x)))^2+ln(1/(2sqrt(x))) ?
The solution to (1/(2sqrt(x)))^2+ln(1/(2sqrt(x))) is (1/(2sqrt(x)))^2++ln(1)-(ln(2)+ln(sqrt(x)))