Questions about Maths questions since I'm a maths noob? (1 Viewer)

[MathsN00b]

I'm working through inverse functions now and I'm getting a bit confused with inverse functions of exponentials and logs.

Is exponential(e) the opposite of loge? (Just want to make sure)

For example, y = e^x
Ans: f^-1(x) = logex or lnx (according to txtbk)

So I'm having difficulty with this question:

y = e^2x

The answer is y = (logex)/2

I'm confused with how the x is on the numerator and the 2 is in the denominator.
Can someone explain to me how this works?

 

[Silly Sausage]

refer to basic logs laws

swap x with y

 

[integral95]

To obtain the inverse function, you swap the x and y and then make y the subject.

you need to know the log law

so from y = e^x, you swap x and y to get x = e^y , then take the log of both sides to get

so idea applies for y = e^2x like this

 

[MathsN00b]

Thanks for the help guys. But would this same method apply for finding the inverse function of y = lnx?

 

[InteGrand]

Thanks for the help guys. But would this same method apply for finding the inverse function of y = lnx?

Yes