Question

If f(x)= 10^x, show that f(x+h)-f(x)/h=10^x(10^h-1/h

Answer 1

Note that, since f(x) = 10^x:
f(x + h) = 10^(x + h).

So, we see that:
[f(x + h) - 10^x]/h = [10^(x + h) - 10^x]/h = (10^x*10^h - 10^x)/h.

Factoring out 10^x gives:
[f(x + h) - 10^x]/h = (10^x*10^h - 10^x)/h = 10^x(10^h - 1)/h, as required.

I hope this helps!