What is ln(2)+xln(x)+sqrt(x)-2ln(x-1)-3 ?

The solution to ln(2)+xln(x)+sqrt(x)-2ln(x-1)-3 is ln(2/((x-1)^2))+xln(x)+sqrt(x)-3

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simplify ln(2)+xln(x)+sqrt(x)-2ln(x-1)-3

simplify

ln (2) + x ln (x) + x - 2 ln (x - 1) - 3

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

Solution steps

ln (2) + x ln (x) + x - 2 ln (x - 1) - 3

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (\frac{x ^{2} x ^{2} + 7}{( x + 7 ) ^{9}})

lo g_{10} (\frac{x ^{4} y}{z})

lo g_{7} (4 yz)

What is ln(2)+xln(x)+sqrt(x)-2ln(x-1)-3 ?
The solution to ln(2)+xln(x)+sqrt(x)-2ln(x-1)-3 is ln(2/((x-1)^2))+xln(x)+sqrt(x)-3