What is 1/2 ln(x)+1/2 ln(x-1) ?

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

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

simplify

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

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

Solution steps

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

ln (\frac{2 x}{x + 3})

\frac{1}{4} [5 lo g_{10} (x) + lo g_{10} (y)]

lo g_{z} (5 z (z - 5)^{5})

lo g_{8} (\frac{( ab ) ^{3}}{c ^{5}})

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