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

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

Popular >

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3 lo g_{10} (3) - 2 lo g_{10} (6)

\frac{1}{4} lo g_{10} (2 x + y) - lo g_{10} (3 x + 2 y)

lo g_{9} (10) - lo g_{9} (7)

ln (\frac{e ^{9}}{12})

lo g_{10} (\frac{x ^{2} y ^{5}}{z ^{3}})

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