Question

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

Answer 1

`x = 2`

Explanation:

We seek a solution of:

`9^(2x) = 3^(2x+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 -oo`

We can examine this analytically, as:

`9^(2x) = 3^(2(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]}