Question

Find the equation of the tangent line of y=5^x and x=1. Round your answer to one decimal place.

I'm guessing I need to know y'=ln(5) * 5^x?
But I'm not sure what to do after that.

Answer 1

So at x = 1, y' = 5ln5

Answer 2

That means the slope at x = 1 is 5 ln 5

Answer 3

So the equation of the line at x = 1 (y = 5) is

y - 5 = 5ln5(x-1)

Answer 4

Since this needs to equal to y, would that be...

y-5 = 5ln5(x-1)
y= 5ln5(x-1)+5

But it's telling me it's wrong.

Answer 5

Can you just distribute normally?

y= 5 ln (5) (x-1) + 5

I'm guessing ln (5) needs to stay in tact...

Answer 6

yes, ln(5) stays intact as thats a single number called ln(5).

Answer 7

I just left the equation in point-slope form. You can solve for y and write the equation in slope-intercept form.

Answer 8

I'm not sure what to do, really.
I know in slope-intercept it would be y=1/8x - 3.0 but I don't know how to keep that ln(5) intact...

I have one more chance for this problem.

Answer 9

Use 1.6 for ln(5)....as in the directions of this question, it asks to use one decimal place.

Answer 10

Oh, okay. I got it. Thanks!