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znimon
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.
Just laws of exponents: \[(f(x+h)-f(x))/h=(8^{x+h}-8^x)/h=(8^x 8^h-8^x)/h=8^x(8^h-1)/h\]
As i don't know the names of those laws I can't look up videos on them. Will you give me the names?
I always refer to them as the "laws of exponents" ... you can search for this quoted phrase on the web or YouTube.
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).
|dw:1350357859691:dw| So this is what your initial setup should look like when you get everything plugged in :) Make sense? :o
I don't understand what property/properties of exponents allow me to conclude 8^(x + h) = 8^x * 8^h
Hmm it's one of the exponent laws. The product of two terms with the same BASE, can be written as the sum of their exponents. I Dunno what the specific law is called :D It's a good one to remember though. \[a^b*a^c=a^{b+c}\]
We're applying this rule in reverse in this case.
That cleared things up, thanks.