SOLUTION: 9^x-2(3^x+2)+81=0

Question 1176692: 9^x-2(3^x+2)+81=0
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

We'll apply the rule

to say that:

The equation

then becomes

Let
Replace every copy of with

We go from

-----------------------------------
Let's solve for w

Apply the quadratic formula
or

or

or

We run into a problem. The negative under the square root means we'll have complex numbers. I'll assume your teacher hasn't covered the concept yet (please let me know if otherwise)

So because has complex solutions, then so does the original equation

-----------------------------------

Now that I think about it further, it's possible that the equation you were given is instead of . Note how the 2 has moved from being in the exponent and then not in the exponent.

If the 2 is in the exponent, then,

If w = 9, then,

So once again, if the equation you were given was (note the 2 in the exponent), then it leads to the single solution of

We can check this by plugging x = 2 back into the original equation to get...

We get the same thing on both sides, so the answer is confirmed for that equation.

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