Question

What is the solution of the equation exe2x = 4?

Answer 1

@austinL

Answer 2

Is it,

\(e^{2x}=4\)?

Answer 3

or
\(\large e^x e^{2x}=4
\\?\)

Answer 4

@hartnn yeh that

Answer 5

I would rewrite it as,

\(e^{x}\times e^{2x}=4\)

Then take the natural log of each side.

Answer 6

so x * 2x = 4

Answer 7

wouldnt that make x squared ?

Answer 8

Yep, we would have,

\(2x^2=\ln(4)\)

Answer 9

would that be my final answer ? or would it be \[x = \sqrt{ \frac{ \ln4 }{ 2}}\]

Answer 10

That is close, you need to simplify that.

\(\displaystyle x=\frac{\sqrt{\ln(4)}}{\sqrt{2}}\)

Do you know how to do that?

Answer 11

no /:

Answer 12

can i just plug it into my calculator ?

Answer 13

You need to multiply both top and bottom by \(\sqrt{2}\)

Answer 14

i got x = .832 is that right ?

Answer 15

Remember what I said, does it tell you to give a decimal approximation? Do you have choices?

Answer 16

no i have to write out my answer. its an online class

Answer 17

wait what ?

Answer 18

@hartnn wym ?

Answer 19

\(\huge x^m \times x^n = x^{m+n}\)

Answer 20

It is \(x\times2x=2x^2\)
@hartnn

Answer 21

\(\huge e^x \times e^{2x} = e^{x+2x}\)

Answer 22

x+2x = ln 4
x = (ln 4) /3

Answer 23

im soooo lost

Answer 24

Oh my goodness.....
I can't believe I made that error...

Answer 25

hartnn is correct.

Answer 26

where do i have to go back and check ?

Answer 27

which step did u not get ?

Answer 28

you confused me ,

Answer 29

okay so ln on both sides gives me x * 2x = 4ln right ?

Answer 30

ln 4 i mean

Answer 31

how x*2x ?

Answer 32

I made an error, it is,

x+2x=ln(4)
3x=ln(4)

Answer 33

x=ln(4)/3

Answer 34

why plus ?

Answer 35

\(\huge x^m \times x^n = x^{m+n}\)

Answer 36

Because I made an error. Go back and look at hartnn's posts.

Answer 37

oh i see

Answer 38

so 3x = 4ln

Answer 39

so e^x e^2x = e^ (x+2x)
only then you take natural log on both sides

Answer 40

3x = ln 4

Answer 41

i take natural log to bring the x's down right ?

Answer 42

yes

Answer 43

and the fact that ln e =1

Answer 44

so my answer is ln 4 / 3 and i have the choice to make it a decimal im guessing ?

Answer 45

We have,

\(\large{e^{x}\times e^{2x}=4\Rightarrow e^{x+2x}=4}\)

Then you take the natural log,

\(\large{x+2x=\ln(4)\Rightarrow3x=\ln(4)}\)

\(\large{\displaystyle x=\frac{\ln(4)}{3}}\)

Answer 46

I would leave it as is, that is the exact answer.

Answer 47

Good catch @hartnn
I made a silly error and you saw it, I would have guided them along the wrong path.... Silly me.

Answer 48

no problem, thats what we call team work :)

Answer 49

wow thanks so muuch !

Answer 50

highly appreciate it