Question

Use logarithms to solve:
e^2x-e^x-110=0

Answer 1

Explanation:

`e^(2x) -e^x-110=0\\put ~e^x=t\\squaring\\e^(2x)=t^2\\t^2-t-110=0\\t^2-11t+10t-110=0\\t(t-11)+10(t-11)=0\\(t-11)(t+10)=0\\either\\t=11\\e^x=11\\taking ~log\\x=log11\approx 1.04\\or\\e^x=-10\\rejected\\as~e^x > 0`