Question about difference quotient with exponents (pre-calculus)

Question

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

As a function of x, the difference quotient of 10^x is 10^x multiplied by a constant.

I have been looked through all my lecture notes and many math websites for an hour and a half now and cannot figure this question out. So far I have gotten to:
= 10^x+h - 10^x/h

I would really appreciate some help with this.

Answer 1

f(x) = 10^x

 

f(x+h) = 10^x+h

 

f(x)/h = 10^x/h

 

f(x+h)-f(x)/h

= 10^x+h - 10^x/h

 

note that x^a+b = x^a(x^b)

 

= 10^x(10^h) - 10^x/h

 

Factor 10^x out of both terms

 

= 10^x[10^h - 1/h]