Can someone explain the One-to-One Property to me? And how I would use it to solve an equation for x?

For example:
45) 3^x+1=27

Question

Can someone explain the One-to-One Property to me? And how I would use it to solve an equation for x? 

For example:
45) 3^x+1=27

anonymous · Answer

@DisplayError

displayerror · Answer

The one-to-one property says that if we're given a logarithmic function like this:
$$5^{x-1} = 25$$
And we can change the base of the right side to be the same as that on the left side,
$$5^{x-1} = 5^2$$
We can just set the exponents equal to each other to solve:
$$x - 1 = 2$$
$$x = 3$$
The same can be done with logarithms. As long as the base is the same
$$\log_5 8 = \log_5 (2x+2)$$
We can set the argument of the logarithms to be equal in order to solve:
$$8 = 2x+2$$
$$x = 3$$

Now for your given problem, we can apply the same idea
$$3^x + 1 = 27$$
Recall your exponents with base 3:
$$\begin{array}{rcr} 3^0 & = & 1 \ 3^1 & = & 3 \ 3^2 & = & 9 \ 3^3 & = & 27\end{array} $$
With this information, you should be able to rewrite your equation such that they're all of the number 3 raised to an exponent. Then you should be able to solve for x using the one-to-one property.

anonymous · Answer

Ok.... that kind of explains it. Lol I'm still kinda confused. I think I might just ask my teacher to explain it to me tomorrow. Thanks anyways :)