Question

How would you write the following expression as a single term? 3[2 ln(x-1) - lnx] + ln (x+1)

Answer 1

Apply the rule:
`n ln x = ln x^(n)`

`3[2 ln(x-1) - lnx] + ln(x+1)=3[ln(x-1)^(2) - lnx ] + ln(x+1)`

Apply the rule :
`log a - log b = log (a)/(b)`

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

Apply the rule:
`n ln x = ln x^(n)`

`3[ln (x-1)^(2) -ln x]+ln (x+1)= ln ((x-1)^(6) )/(x^(3) ) +log(x+1)`

Finally, apply the rule: log a + log b = log ab

`3[ln(x-1)^(2) -ln x]+log(x+1)=ln((x-1)^(6)(x+1) )/(x^(3) )`