Tuesday
May 21, 2013

Posted by Anonymous on Wednesday, January 27, 2010 at 8:55am.

Solve

3^2x + 3^x - 21

check extraneous roots

• math please - drwls, Wednesday, January 27, 2010 at 9:09am

Is the first term 3^2x (which is 9x) or 3 x^2 or 3^(2x)?

You have not stated an equation, only a function definition or "expression". There is nothing to "solve"

The solution to
3^(2x) + 3^x -21 = 0 is about x = 1.29

• math please - Anonymous, Wednesday, January 27, 2010 at 9:18am

how was it solved ? quad formula. what is a b and c?

• math please - drwls, Wednesday, January 27, 2010 at 9:42am

If you are talking about using a quadratic formula, you wrote the equation wrong. As i said before, you did not even write and equation

It should have been 3x^2 + 3x -21 = 0, whic is the same as x^2 +x -7 = 0
That equation has only irrational roots.

I solved the other equation by trial and error.

• math please - drwls, Wednesday, January 27, 2010 at 11:14am

Here is a way to solve
3^(2x) + 3^x -21 = 0
Let 3^x = y
Then,
y^2 + y -21 = 0
b^2 -4ac = 85
The roots are:
y = [-1 +/- sqrt 85]/2
= -5.1098 or 4.1098
When y = 4.1098,
x = (lny)/ln3 = 1.2865
I mentioned that solution in a previous post.

There is another "y" solution corresponding to y = -5.1098
However that appears to require the log of a negative number, which has no real solution for x.

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