How do you simplify #ln (e* e * e)#?

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
George C.
Oct 25, 2015

#ln(e*e*e) = ln(e^3) = 3#

Explanation:

Natural logarithm #ln(x):(0, oo)->RR# and the natural exponential function #e^x:RR->(0, oo)# are inverses of one another.

So #ln(e^x) = x# for #x in RR# and #e^(ln(x)) = x# for #x in (0, oo)#

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