8. If we solve the equation 4e^ 2x = ln 2, then to 3 significant digits x is approximately:?

Question

how do i solve this... they give me the answer .876 and i got a totally different answer of .093! whats up?

okay, that sort of helps, but i am not sure how to type that into my calculator, it keeps telling me error! Thanks

Answer 1

e^(2x) = ln2 / 4
2x = ln(ln2) - ln(4)
x = -0.8764

Answer 2

The solution to what you wrote:
4e^2x = ln 2
x = ln(2)/(4e^2) = 0.0235

I'm guessing what you really meant was:
4e^(2x) = ln(2)
e^(2x) = ln(2)/4
(2x) = ln[ ln(2)/4]
x = ln[ ln(2)/4] / 2
x = -0.876

Answer 3

4e^ 2x = ln 2

e^2x = (ln2)/4

ln(e^2x) = ln{(ln2)/4}
2x = ln{(ln2)/4}
x = 0.5ln{(ln2)/4}= -0.876