How do you condense #ln(x^(3) - 8) - ln(x^(2) + 2x + 4) + ln(x + 2)#?

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Answer 1 · 2018-07-09T18:39:19

#ln(x^2-4)#

We get

#ln(x^3-8)+ln(x+2)=ln((x^3-8)(x+2))#
after the law: #ln(a)+ln(b)=ln(ab)# for #a,b>0#

then we get

#ln(((x^3-8)(x+2))/(x^2+2x+4))#
now we use that

#a^3-b^3=(a-b)(a^2+ab+b^2)#
so we get

#x^3-8=(x-2)(x^2+2x+4)#
after cancelling like Terms we get

#ln(x^2-4)#