SOLUTION: Solve the equation To clarify on the 1/3^x the denominator has the exponent not the whole fraction, I'm not sure if that matters. Thank you!

Question 974196: Solve the equation
To clarify on the 1/3^x the denominator has the exponent not the whole fraction, I'm not sure if that matters. Thank you!
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!

Multiply by 3^x

Sub u for 3^x

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=140 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 11.9160797830996, 0.0839202169003839. Here's your graph:

=======================
3^x = 11.919
x*log(3) = log(11.919)
x = log(11.919)/log(3)
===========================
Do the other 3^x root the same way.
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