Question

Solve for x.
6e^2x = 7e^4x

Answer 1

do you have multiple choice questions for this? and are we using E as a variable or as a number?

Answer 2

\(\Large 6e^{2x} = 7 e^{4x} \)?

Answer 3

@noseboy908

Answer 4

Have you considered what @YoloShroom and @Luigi0210 have said?

Answer 5

No multiple choice. e as in natural log. and waht @Luigi0210 is my problem.

Answer 6

Sorry, this is beyond me. Could you assist, @YoloShroom ?

Answer 7

yeah let me take a look.

Answer 8

You're gonna need to take the logs of both sides, have you tried that?

Answer 9

it could be x= 0, because the bases are the same, we can set the exponents to equal each other i believe.
SO it may just be 2x=4x, then 2x=0, x=0.

Answer 10

@Luigi0210 I haven't tried taking the logs. How would I do that?
@YoloShroom How are the bases the same?

Answer 11

you have the Natural log as both the bases, ^_^
May be wrong, just a suggestion.

Answer 12

Oh, I was just confused cause I thought the 7 and the 6 were the bases. If the e's are the bases then they cancel each other out?

Answer 13

You can take the logs of both sides like this:

\(\Large \color{red}{log}(6e^{2x} ) = \color{red}{log} (7e^{4x} ) \)

Now you can apply log rules:

\(\Large log(6)+log(e^{2x}) = log(7)+log(e^{4x} ) \)

Make sense so far?

Answer 14

OH GOD, i forgot the base rule.. my bad. Good call

Answer 15

Here's a hint: \(\large log(e^x) = x \)

Answer 16

Okay. That makes sense.

Answer 17

You should end up with \(\Large log(6) +2x = log(7)+4x \)

Get like terms on the same side: \(\Large -2x=log(7)-log(6)\)

Now just divide both sides by -2 and you'll get your x \(\Large \ddot \smile \)

Answer 18

I got x = -0.033

Answer 19

@Luigi0210

Answer 20

I think it's best to leave it as \(\Large x=-\frac{log(7)}{2}+\frac{log(6)}{2} \)

But if you need a decimal then -0.0335 should work :)

Answer 21

Okay. Thank you!

Answer 22

No problem :)