Question

If f(x)=10^x show that

f(x+h)-f(x)
--------- = 10^x((10^h -1)/h)
h

Answer 1

Let\[f(x)=10^x.\]Then\[\frac{f(x+h)-f(x)}{h}=\frac{10^x\cdot10^h-10^x}{h}=\frac{10^x(10^h-1)}{h}.\]

Answer 2

The key law here is\[a^{b+c}=a^b\cdot a^c.\]

Answer 3

i still dont quite understand it tho...

Answer 4

It is very clear:\[f(x+h)=10^{x+h}=10^x\cdot10^h.\]