How do you solve #9^(2x)=3^(2x+4)# using a graph?
1 Answer
Oct 12, 2017
# 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
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]}