Question

e^2x-1 + 5 =8

Answer 1

first step, simplify the expression, so move all the 'like' terms to the same side of the equation

Answer 2

is it e^(2x)-1 + 5 or e^(2x-1) + 5

Answer 3

?

Answer 4

the second one

Answer 5

great,
e^(2x-1) + 5 = 8,
we need to simplify the expression by combining all the 'like' terms, post up what you get

Answer 6

i think i did it wrong but lne^(2x-1) =ln3

Answer 7

close, we do want to use ln, but we want to use the 'definition of logs' to get the x out of the exponent's place. are you familiar with the 'definition of logs'?

Answer 8

\[e^{n} = m \rightarrow \ln(m) = n\]

Answer 9

Yah that method works fine Ms Teisha :)
\[\Large \ln e^{(2x-1)}\quad=\quad(2x-1)\ln e\quad=\quad (2x-1)\cdot1\]So that's how your left side would simplify.
It's a little bit more cumbersome than simply remembering how to rewrite something in log form as Demolish demonstrated, but still works fine.

Answer 10

so take your equation:
e^(2x-1) =3
and apply this rule that looks like this:
\[e^{n}=m→\ln(m)=n\]
so pick out what terms in your equation looks like the 'n' and the 'm'

Answer 11

I have no idea!. . . . .

Answer 12

If I said
n = (2x-1)
can you pick out
m = ?

Answer 13

do you see how they are similar? the 'form' and your equation?

Answer 14

so is it in ( 3) = 2x-1 ???

Answer 15

yep! just don't forget the ln, so like this:
ln(3) = 2x-1

now isolate the x, or in other words, get all the 'non' x numbers to the opposite side of x.

Answer 16

first move the 1 over to the other side

Answer 17

is x 2?

Answer 18

ya so now it looks like this:
ln(3) + 1 = 2x
then just divide both sides by 2

Answer 19

so 2 right?

Answer 20

ya,
so what now our equation looks like this:
x= ( ln(3) + 1 ) / 2

Answer 21

Is that the final answer?

Answer 22

yep, good job!

Answer 23

good job to you. I didn't do anything lmao