SOLUTION: Solve for x, π⁴ˣ - 10π²ˣ + 9 = 0

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Question 1210346: Solve for x,
π⁴ˣ - 10π²ˣ + 9 = 0
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve for x,
pi%5E%284x%29 - 10%2Api%5E%282x%29 + 9 = 0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

I will assume that, by default, the designation  pi  is used in its standard meaning 

as the ratio of the circle circumference to its diameter,  pi = 3.14159265...


Factor left side of the equation

    %28pi%5E%282x%29-1%29%2A%28pi%5E%282x%29-9%29 = 0.


Then EITHER  pi%5E%282x%29 = 1,  which gives  2x = 0,  x = 0;

     OR      pi%5E%282x%29 = 9,  which gives  2x = log%28pi%2C%289%29%29 = 2%2Alog%28pi%2C%283%29%29,  

             x = log%28pi%2C%283%29%29 = 1%2Flog%283%2C%28pi%29%29 = 1%2Flog%283%2C%283.14159265%29%29 = 1%2F1.041978045 = 0.95971312  (rounded).    ANSWER


ANSWER.  Two solutions are  x= 0  and/or  x = 1%2Flog%283%2C%28pi%29%29 = 0.95971312  (rounded).

Solved.