What is simplify-ln(u)+1/2*ln(u-1)+1/2*ln(u-1) ?

The solution to simplify-ln(u)+1/2*ln(u-1)+1/2*ln(u-1) is ln((u-1)/u)

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simplify-ln(u)+1/2ln(u-1)+1/2ln(u-1)

simplify

- ln (u) + \frac{1}{2} \cdot ln (u - 1) + \frac{1}{2} \cdot ln (u - 1)

ln (\frac{u - 1}{u})

Solution steps

- ln (u) + \frac{1}{2} ln (u - 1) + \frac{1}{2} ln (u - 1)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{( u - 1 ) ^{\frac{1}{2}}}{u} (u - 1)^{\frac{1}{2}} : \frac{u - 1}{u}

= ln (\frac{u - 1}{u})

ln (\frac{1}{x ^{6}})

ln (\frac{y cos ( y )}{d y})

- lo g_{10} (3.3333 \cdot 1 0^{- 3})

lo g_{10} (p^{x} \cdot (1 - p)^{1 - x})

ln (x^{2} + 10 x + 24) - ln (x + 6)

What is simplify-ln(u)+1/2*ln(u-1)+1/2*ln(u-1) ?
The solution to simplify-ln(u)+1/2*ln(u-1)+1/2*ln(u-1) is ln((u-1)/u)