Question

Question #bbbe5

Answer 1

Given `3^(2x+1)+26(3^x)-9 =0` the solution is `x=-1`.

Explanation:

Note: I suspect there's a typo in the question because this has a very similar form to a very common question, so I'm going to go with the common form in my response.

Given `3^(2x+1)+26(3^x)-9 =0` we can first rewrite a `3^(2x+1)` as `3*(3^x)^2` using properties of exponents.

So now we have the equation:

`3*(3^x)^2+26(3^x)-9 =0`

Let `u=3^x` and this becomes:

`3u^2+26u-9=0`

We can factor that:

`(3u-1)(u+9)=0`

So either `u=1/3` or `u=-9`

Substituting for `u` again:

`3^x=1/3 rarr x=-1`

`3^x = -9` which has no solutions.

So `x=-1` is the only solution.