Solve: 3^2x-1+1 = 2

Question

Solve: 3^2x-1+1 = 2

anonymous · Answer

The -1 and +1 cancel, leaving 3^(2x) = 2. Since they have different bases, the only thing we can do is log both sides to bring down the exponent (which has the variable). That would yield 2x*log (3) = log (2). Divide both sides by 2 log (3) and our answer would be

$$x=\log2/(2\log3)$$

anonymous · Answer

Now, if the problem was actually $$3^{2x-1}+1=2$$ We could first subtract one to get $$3^{2x-1}=1$$ Then, rewriting both sides as base 3, we would get $$3^{2x-1}=3^{0}$$ Thus, both sides would have the same base, so we can set 2x-1 = 0 and find that x=1/2.

anonymous · Answer

Oh ok! yes it was written in the way you mentioned second, I was not sure of how to write it. I for some reason keep wanting to change both sides with an additional exponent.
Thanks

anonymous · Answer

You are welcome. As soon as I finished the first answer, it hit me what you must have meant. :)