Question

solve e^2x-1 = 3 for x

Answer 1

Is this

\[\large e^{2x - 1} = 3\]
or
\[\large e^{2x} - 1 = 3\]

Answer 2

e^(2x-1) = 3

Answer 3

Alright

\[\large e^{2x - 1} = 3\]

Remember the rules for logarithms...\(\large ln(e^{ax}) = ax \times ln(e)\)

So if we apply this here, and take the log of both sides...we have

\[\large ln(e^{2x - 1}) = ln(3)\]
which then turns into
\[\large (2x - 1)ln(e) = ln(3)\]
Still with me?

Answer 4

I am

Answer 5

Great...what is \(\large ln(e) = ?\)

Answer 6

1?

Answer 7

Right!

So we really just have

\[\large (2x - 1) = ln(3)\]

Now just solve that for 'x'

Answer 8

Ln3 +1 / 2

Answer 9

Right! *just to make sure you mean all over 2 though...