What is 1/2 ln(x)-3ln(x-1) ?

The solution to 1/2 ln(x)-3ln(x-1) is ln((x^{1/2})/((x-1)^3))

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simplify 1/2 ln(x)-3ln(x-1)

simplify

\frac{1}{2} ln (x) - 3 ln (x - 1)

ln (\frac{x ^{\frac{1}{2}}}{( x - 1 ) ^{3}})

Solution steps

\frac{1}{2} ln (x) - 3 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}}) - 3 ln (x - 1)

Apply log rule:

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

3 ln (x - 1) = ln ((x - 1)^{3})

= ln (x^{\frac{1}{2}}) - ln ((x - 1)^{3})

Apply log rule:

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

ln (x^{\frac{1}{2}}) - ln ((x - 1)^{3}) = ln (\frac{x ^{\frac{1}{2}}}{( x - 1 ) ^{3}})

= ln (\frac{x ^{\frac{1}{2}}}{( x - 1 ) ^{3}})

7 ln (x) - \frac{1}{6} ln (y)

ln (\frac{cos ( x )}{cos ( x ) - 1})

ln (2) - ln (7)

What is 1/2 ln(x)-3ln(x-1) ?
The solution to 1/2 ln(x)-3ln(x-1) is ln((x^{1/2})/((x-1)^3))