# Use the proper steps of simplification to solve this equation for all valid values of x: `3^2x + 1 = 4` Then redo the problem for this expression `3^(2x) + 1 = 4`

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### 1 Answer

The first equation is a straight forward simplification equation where one needs to "undo" the order of operations in order to get the solution.

The normal order of operation would be to do powers, multiplication and division, and finally add and subtract. To solve an equation we reverse this order. In the first example we would

subtract 1 from both sides to undo the +1

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then undo the multiplication by dividing by `3^2`

`x = 3/3^2 = 1/3`

We can check our work by substituting this value back into the original equation:

`3^2 (1/3) + 1 = 3^2/31 = 3 + 1 = 4`

To do the second equation we must get the variable out of the exponent which means we must take the logarythm of both sides of the equality

`3^(2x) + 1 - 1 = 4 - 1`

`3^(2x) = 3`

`log(3^(2x)) = log(3)`

2x = 2

`x = 1/2`

Again, we can check by substitution:

`3^(2(1/2)) + 1 = 3^1 + 1 = 3 + 1 = 4`