SOLUTION: Given that 3^x=9^x+1 work out the value of x. My wrong workings: 3x=9x+1 X+1squareroot 3x=9 X=9-x+1squareroot3x

Algebra ->  Square-cubic-other-roots -> SOLUTION: Given that 3^x=9^x+1 work out the value of x. My wrong workings: 3x=9x+1 X+1squareroot 3x=9 X=9-x+1squareroot3x      Log On


   

Question 980846: Given that 3^x=9^x+1 work out the value of x.
My wrong workings:
3x=9x+1
X+1squareroot 3x=9
X=9-x+1squareroot3x
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
9%5Ex-3%5Ex=-1
%283%5E2%29%5Ex-3%5Ex=-1
%283%5E%282x%29%29-3%5Ex=-1
%283%5Ex%29%5E2-3%5Ex=-1
%283%5Ex%29%5E2-3%5Ex%2B1=0

Pick an arbitrary new variable.
Let p=3%5Ex, and rewrite the equation as
p%5E2-p%2B1=0

Now first solve this equation for p.

p=%281%2B-+sqrt%281%5E2-4%2A1%2A1%29%29%2F2 according to general solution of a quadratic equation.
p=%281%2B-+sqrt%28-3%29%29%2F2
p=%281%2B-+i%2Asqrt%283%29%29%2F2

Next substitute for p.
3%5Ex=%281%2B-+i%2Asqrt%283%29%29%2F2, a complex result, still unfinished.
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Unless I made a mistake in the process, this is not a beginner's exercise. Maybe another tutor can carry this to a solution for x.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Given that 3^x=9^x+1 work out the value of x.
My wrong workings:
3x=9x+1
X+1squareroot 3x=9
X=9-x+1squareroot3x
It must be 3%5Ex+=+9%5E%28x+%2B+1%29. You need to USE PARENTHESES. Write back and I'll solve in detail if I have the time. 

In the meanwhile, the solution is: highlight_green%28x+=+-+2%29 because anything else does not make any sense.

It's simple, as in: 3^x = 9^(x + 1). Understand?