Question

solve the equation for x. e^7-4x=6

Answer 1

You mean,
\[e^{7-4x}=6?\]

Answer 2

Yes, that's correct.

Answer 3

I'm not sure how to go about solving this problem.

Answer 4

Do you know about logarithms?

Answer 5

I give you a hint. One of the properties of logarithms is
\[\log(a^n)=n\log(a)\]
So you can employ that in an equation like this,
\[a^n=b\Rightarrow n\log(a)=\log(b)\]

Answer 6

Well, yeah I guess so. I think that I should find a common base so that i can cancel them out and set the exponents to each other but i'm not sure, I could be wrong.

Answer 7

It would be better to use natural logarithms, because
\[\ln(e)=1\]

Answer 8

Yes, I see that log is the inverse or is comparable to log, so using the equation would you get (7-4x)log(6)?

Answer 9

Well,
\[\ln(e^{7-4x})=\ln(6)\Rightarrow 7-4x=\ln(6)\]
You missed an =.

Answer 10

Then solve for x.

Answer 11

oh okay! well thank you very much John_ES I can solve from here!

Answer 12

;)