How do you condense #4[ln x + ln(x +5)] - 2 ln(x - 5)#?

1 Answer
Shwetank Mauria
Sep 2, 2016

#4[lnx+ln(x+5)]-2ln(x-5)=ln((x^4(x+5)^4)/((x-5)^2))#

Explanation:

We should use the identities #loga+log=log(a×b)#, #loga-log=log(a/b)# and #nloga=log(a^n)#.

Hence #4[lnx+ln(x+5)]-2ln(x-5)#

#4lnx+4ln(x+5)-2ln(x-5)#

= #lnx^4+ln(x+5)^4-ln(x-5)^2#

= #ln((x^4(x+5)^4)/((x-5)^2))#

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