How do you expand # ln sqrt (( x^2( x+2))#?

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Answer 1 · 2016-05-30T21:33:32

For this problem, you must remember that #sqrt(x) = x^(1/2)#

#ln(x^2(x + 2))^(1/2)#

Using the product rule (#log_an + log_am = log_a(n xx m)#) and distributing.

#=ln(x^2)^(1/2) + ln(x + 2)^(1/2)#

Using exponent rules to simplify #((x^2)^(1/2) =x^ (2 xx 1/2) = x^1#)
#=lnx + ln(x + 2)^(1/2)#

Now use the log rule #logn^a = alogn#

#=lnx + 1/2ln(x + 2)#

Hopefully this helps!