How do you condense #3 [ln(x) - 2ln(x^2 + 1)] + 2ln(5)#?

1 Answer
Mar 21, 2018

Answer:

#ln((25x^3)/(x^2+1)^6)#

Explanation:

We have,

#color(red)((1) .lnX^n=nlnX#

#color(red)((2).ln(X*Y)=lnX+lnY#

#color(red)((3).ln(X/Y)=lnX-lnY#
Now,
#3[lnx-2ln(x^2+1)]+2ln(5)#
#=3[lnx-ln(x^2+1)^2]+ln(5)^2...to#,Apply(1)
#=3[ln(x/((x^2+1)^2))]+ln(25)....to# Apply(3)
#=ln((x/(x^2+1)^2)^3)+ln25#
#=ln(x^3/(x^2+1)^6)+ln25#
#=ln(25*x^3/(x^2+1)^6)...to# Apply(2)
#=ln((25x^3)/(x^2+1)^6)#