What is 1/2 ln|x|-2ln|1-sqrt(x)| ?

The solution to 1/2 ln|x|-2ln|1-sqrt(x)| is ln((|x|^{1/2})/((1-sqrt(x))^2))

Popular >

simplify 1/2 ln|x|-2ln|1-sqrt(x)|

simplify

\frac{1}{2} ln ∣ x ∣ - 2 ln 1 - x

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

Solution steps

\frac{1}{2} ln ∣ x ∣ - 2 ln 1 - x

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

1 - x^{2} = (1 - x)^{2}

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

lo g_{10} (14.22) + lo g_{10} (0.11)

- lo g_{10} (8.5 x 1 0^{- 6})

10 lo g_{6} (c) + 10 lo g_{6} (a) - 2 lo g_{6} (b)

\frac{3}{5} \cdot (- \frac{2}{3} lo g_{e} (\frac{2}{3}) - \frac{1}{3} lo g_{e} (\frac{1}{3}))

3 ln (a) + ln (b) - ln (c)

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