Step-by-Step Solution of f(x)=5^x

[wtfpurepwned]

If f(x)= 5^x, show that

f(x+h) - f(x) / h = (5^x)(((5^h)-1) / h)

I need a step by step solution or some hints

 

[Dickfore]

Do you know any properties of the exponential function?

 

[wtfpurepwned]

like the law of exponents? i know most of them. ill apply the laws more thoroughly

 

[Dickfore]

Do you think the term "exponential function" has anything to do with the problem you have posed?

 

[wtfpurepwned]

yes, when i see something like 5^x

 

[Dickfore]

So, can you state some of the properties of the exponential function?

 

[wtfpurepwned]

http://www.efunda.com/math/exp_log/exp_relation.cfm

got lazy :)

 

[Dickfore]

Ok, so, if $f(x) = 5^{x}$, which one of those would you use (and in what direction, i.e. from left to right or right to left) to express $f(x + h)$?

 

[wtfpurepwned]

not sure which one would work for that since i only understand the first 4-5 properties atm but if i have to do something id go with f(x+h) = 5^x + 5^h and that doesn't seem to make a whole lot of sense

 

[Dickfore]

not sure which one would work for that since i only understand the first 4-5 properties atm but if i have to do something id go with f(x+h) = 5^x + 5^h and that doesn't seem to make a whole lot of sense

Hint:
$$f(x + h) = 5^{x + h}$$

not $5^{x} + 5^{h}$.

If you are not comfortable with this, I think you need to brush on your pre-calc syllabus.

 

[wtfpurepwned]

okay i see how it works out now. didn't take calc after high school pre-calc and it's been 3 years, everything is in bit's and pieces..I'm currently brushing my *** off :( thanks for the help Dick