Fan And medal if you can help me (attached)

Question

anonymous · Answer

attachment

mertsj · Answer

Replace 8 with 2^3 and use the principle that if the expressions are equal and the bases are the same, then the exponents must be equal

anonymous · Answer

can you explain that i know that we went over the principle but our teacher wanted us to actually write this out

mertsj · Answer

Did you replace 8 with 2^3?

mertsj · Answer

Post what you get when you do that.

anonymous · Answer

im lost shouldn't i have 2^2x = (2^3)^x-1?

mertsj · Answer

$$2^{2x}=(2^3)^{x+1}$$
$$2^{2x}=2^{3x+3}$$

anonymous · Answer

what? is it because of the negative 3?

mertsj · Answer

I thought you had it right.  In your post you have x-1.  That is incorrect.  The problem shows x+1 so my post is correct.

anonymous · Answer

oh so its my typo ok, so i know that in other problems something like x = ? would be the result if they have the same base

mertsj · Answer

Are the bases the same?

anonymous · Answer

but in this one i think:

2^2x = 2^3x + 3
2x = 3x + 3
-1x = 3
x = -3

right?

mertsj · Answer

Yes.  They are both 2
Are the expressions the same?
Yes.  There is an equal sign between them

mertsj · Answer

Yes.  x = -3

anonymous · Answer

Thank you! :)