Quick Question about Logarithms and Exponents

I have an assignment question looks like this

I figured, first time around, that I could just apply natural logarithm to both, and get

and then x = ln(5)/-4

This does not result in the correct answer.

Why? I can get the correct answer (by dividing both sides by two initially)

If I have 2e^(-2x) and apply the natural logarithm to it, what does it become?

Re: Quick Question about Logarithms and Exponents

Divide through by 2 first, then convert from exponential to logarithmic form.

If you take the natural log of both sides, you have:

Same as if you had just divided through by 2 initially.