Function with ln and e

f(x)=2x+ln2
g(x)=e^2x

Prove that the composite function gf(x)=4e^4x

So far: gf(x)= g(2x+ln2)

= e^2(2x+ln2)

=(e^4x)(e^2ln2)

and 2ln2 = ln4

but not sure this is what they want!? ...is my proof totally finished, given it's worth 4 marks.

Reply 1

yusufu

It's correct, although you might want to finish off with:
=(e^4x)(e^2ln2)
=4e^4x

Reply 2

Lawbutwhere?

=(e^4x)(e^2ln2)
=4e^4x

please explain exactly why this is so- all i can see it that you plus the powers, and 2ln2 = 4, but don't fully get how its exactly 4e^4x

sorry and thanks

Reply 3

__WiZaRD__

Because e^2ln2 = 4

Therfore:
(e^4x)(e^2ln2)
=(e^4x)4
=4e^4x

Reply 4

Christophicus

Lawbutwhere?

=(e^4x)(e^2ln2)
=4e^4x

please explain exactly why this is so- all i can see it that you plus the powers, and 2ln2 = 4, but don't fully get how its exactly 4e^4x

sorry and thanks

e^2ln2 = e^ln2^2 = e^ln4 = 4

Reply 5

Amii

how did u go from

= e^2(2x+ln2)
to
=(e^4x)(e^2ln2) ? i thought it would be (e^4x+2ln2)

Reply 6

wacko_demon

(e^a+b) =(e^a)(e^b)
therefore
e^2(2x+ln2) = (e^4x+2ln2) = (e^4x)(e^2ln2)
and
(e^2ln2) = 4

therefore 4(e^4x) = 4e^4x

not toooo sure but that how i do it
hope it helps

khalid