Master the Exponential Equation: Solving for Y Made Easy!

[GodOfYou]

Exponential Equation! -Stuck!-

1. 3^2y+3 = 3^y+5

The Attempt at a Solution

2y + 3 = y+5
2y = y+2


I really don't think I am doing this right, I am trying to find the value of Y. the answer is 2 but I don't know how to come up with the answer.

 

[pbandjay]

The progress looks great to me! The next step is to get all of the y-terms on one side of the equation.

 

[GodOfYou]

So then would it be 2y + y = 2 or 2y² = 2?

 

[pbandjay]

2y + y = 2 or 2y² = 2

These two equations are not equivalent. Let us ignore the 2y² = 2 for now. Your previous step left the equation at 2y = y + 2. Remember that if you add or subtract a value from one side of the equation, you have to do the same thing to the other side. Therefore, in the first equation in the quote you have 2y + y = 2, but this is not the same as 2y = y + 2 because you added one y to the left side but subtracted the y from the right side. If you add y to the left, then you must add y to the right, getting 2y + y = y + y + 2.

Instead of this, can you think of what to do to both sides of the equation that would result in having no y on the right side of the equation?

 

[apt403]

If $b^x=b^y$, then $x=y$

Remove $b$ from both sides, and you're left with something quite a bit easier to solve.

 

[Mark44]

If $b^x=b^y$, then $x=y$

Remove $b$ from both sides, and you're left with something quite a bit easier to solve.

This is good advice, but the OP has already done this. Take a closer look at the original post.

 

[Mark44]

So then would it be 2y + y = 2 or 2y² = 2?

2y + y and 2y² are very different expressions. The first is (obviously) 2y + y, which is the same as 2y + 1y; the second is 2y*y.

The distributive law says that a(b + c) = ab + ac, or equivalently, that (b + c)a = ba + ca. This second form looks a lot like 2y + 1y.

 

[apt403]

This is good advice, but the OP has already done this. Take a closer look at the original post.

Ahh, sorry about that. I should have looked at the solution attempt more closely.