How do you solve 9^(2x)=3^(2x+4)92x=32x+4 using a graph?

1 Answer
Oct 12, 2017

x = 2x=2

Explanation:

We seek a solution of:

9^(2x) = 3^(2x+4) 92x=32x+4

If we plot both functions on the same graph we have:
graph{ (y-9^(2x)) (y-3^(2x+4)) =0 [-5, 5, -2, 40]}

It appears as if there is no solution, except asymptotically as x rarr -oox

We can examine this analytically, as:

9^(2x) = 3^(2(x+2)) 92x=32(x+2)
:. 9^(2x) = 9^(x+2)
:. 2x = x + 2
:. x = 2

And so we conclude there is indeed a solution, but due to scale we are missing the solution, if we change the scale we get:
graph{ (y-9^(2x)) (y-3^(2x+4)) =0 [-5, 5, -500, 9000]}