# 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]}