How do you condense #ln x-4 ln(x + 2) + 3 ln x#?

1 Answer
Shwetank Mauria
Oct 14, 2016

#lnx-4ln(x+2)+3lnx=ln(x/(x+2))^4#

Explanation:

Some of the basic operations in logarithm are #log_ma+log_mb=log_m(ab)#, #log_ma-log_mb=log_m(a/b)# and #nlog_ma=log_m(a^n)#. Further #ln# is special form where #m=e# i.e. base is #e#. Using them

#lnx-4ln(x+2)+3lnx#

= #lnx-ln(x+2)^4+lnx^3#

= #ln((x×x^3)/(x+2)^4)#

= #ln(x^4/(x+2)^4)#

= #ln(x/(x+2))^4#

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