Expression of single logarithm

Question

How can I express the following as a single logarithm:

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

Answer 1

3lnx -2ln(x-1)+ ln(x+1)^(1/3)

= lnx^3- ln(x-1)^2 + ln(x+1)^(1/3)

=ln((x^3)(x+1)^(1/3)/(x-1)^2)

Answer 2

3ln(x) - 2ln(x-1) + ln (x+1)^1/3 First apply the power rule.

ln x³ - ln (x - 1)² + ln (x + 1)^1/3 Next use the laws for products and quotients.

ln x³(x + 1)^1/3

(x - 1) ²

Answer 3

3lnx + ln(x+1)^1/3 - 2ln(x-1) = ln(x³) + ln(x+1)^1/3 - ln(x-1)²

= ln[x³(x+1)^1/3] - ln(x-1)² = ln[ x³(x+1)^1/3 / (x-1)² ]

Answer 4

See the videa.

Make sure to know the log rules: https://www.chilimath.com/lessons/advanced-algebra/logarithm-rules/