Question

If f(x) = 8^x, show that (f(x+h) - f(x))/h = 8^x((8^h-1)/h)

I am not sure of the properties at play here. I have the answer. If someone would refer some khan academy videos for further explanation that would be appreciated.

Answer 1

Just laws of exponents:
\[(f(x+h)-f(x))/h=(8^{x+h}-8^x)/h=(8^x 8^h-8^x)/h=8^x(8^h-1)/h\]

Answer 2

As i don't know the names of those laws I can't look up videos on them. Will you give me the names?

Answer 3

I always refer to them as the "laws of exponents" ... you can search for this quoted phrase on the web or YouTube.

Answer 4

So the funky looking thing they gave you is called the "Difference Quotient"
Remember back to algebra using the uhhh, ugh i forget what it's called.
To find the slope of a line.\[m=\frac{ y_2-y_1 }{ x_2-x_1 }\]
It's the same thing, it's the slope of a line, given 2 points. But now we're using function notation so it's a little bit fancier :)
The distance between x_2 and x_1, we call that h.
So now our y (which is now f(x)), the second y value will be the FIRST y value + the distance h that we traveled.
f(x+h) - f(x).

Answer 5

So this is what your initial setup should look like when you get everything plugged in :)
Make sense? :o