Question

2^(3x+1)=2^)2/x) I don't know what to do here to get both of the xs

Answer 1

Since you have the same base, do this:

3x + 1 = 2/x

Now we can solve for x:

x(3x + 1) = x(2/x) -->multiplying both sides by x to get rid of x in the denominator. (Whatever operation you do to one side of an equation you must do to the other side as well.)

3x^2 + x = 2

Set the equation equal to 0:
3x^2 + x - 2 = 0

Try to factor:
(3x - 2)(x + 1)

Set each factor equal to 0 and solve for x:
3x - 2 = 0; x = 2/3
x + 1 = 0; x = -1

You have two possible solutions. Check these with the original equation. It always helps to check your work!

I hope this helps.