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

Question

john_es · Answer

You mean,
$$e^{7-4x}=6?$$

anonymous · Answer

Yes, that's correct.

anonymous · Answer

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

john_es · Answer

Do you know about logarithms?

john_es · Answer

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,
$$a^n=b\Rightarrow n\log(a)=\log(b)$$

anonymous · Answer

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.

john_es · Answer

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

anonymous · Answer

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

john_es · Answer

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

john_es · Answer

Then solve for x.

anonymous · Answer

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

john_es · Answer

;)