How do I find a solution to e^{2x}=8e^{x}+20?

Alex Cervantes

Alex Cervantes

Answered question


How do I find a solution to e2x=8ex+20?

Answer & Explanation

Larissa Hogan

Larissa Hogan

Beginner2022-02-02Added 10 answers

Step 1
By properties of exponents, we have:
We let t=ex
t=10 and 2
ex=10 and ex=2
Take the natural logarithm of both sides.
ln(ex=ln10 and lnex=ln2
Use the rule logan=nloga:
xlne=ln10 and xlne=ln2
ln and e are opposites, so equal 1
x=ln10 and x=0, since y=lnx has a domain of x>0

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