Real Exponents and Exponential Functions

[bezdomni]

I missed my math lesson this morning and my book does a terrible job of explaining Exponential Functions. I can understand the basics of simplifying expressions, but the equations and inequalities are pissing difficult.

If anybody can explain how to solve an exponential function and show an example I would be incredibly greatful!

Some of the problems from my homework are:

9^2p=27^p-1

16^n > 8^n+1


I just need to figure out how to solve these equations.

Thanks! :D

[Comrade-Z]

9^2p=27^p-1

(3^2)^2p = (3^3)^p-1

3^4p = 3^(3p-3)

The bases are the same, so the exponents on each side are equivalent:

4p = 3p - 3

p = -3


16^n > 8^n+1

(2^4)^n > (2^3)^(n+1)

2^4n > 2^(3n + 3)

Once again, the bases are the same, so they can drop out of the equation.

4n > 3n + 3

n > 3

The trick with these is to recognize the base that both sides can be reduced to. With the first example, both sides can be both in terms of 3^x where x is some number. In the second example, both sides can be put in the form 2^x. After that, it's just about remembering the addition/subtraction of exponents rule and the "power to a power" rule (exponents taken to a power are multiplied to that power number--and don't forget to use the distributive property). For example, 3^2^(5n+4) becomes 3^(2(5n + 4)) and so on.

[bezdomni]

Thank you a hundred times comrade!

Math textbooks in Texas generally suck. ;)

:D

[Janus]

Yes, as Comrade Z showed you, the most important thing is to reduce the term that is being taken to a power. This will allow you to figure out things much easier.