In an integration exercise, I'm trying to find the points of intersection for two functions. The two functions are:
d(x) = 3^x
f(x) = -2x+5
I set them to being equal, and then took the log of both sides. (The x exponent on 3^x jumps in front because of the logarithm identities)
3^x = -2x+5
xlog3 = log(-2x+5)
Now I am stuck, and I'm not sure of what to do. I would really appreciate anybody's assistance.
You can't solve this using algebra but by inspection I find that is a point of intersection
Edit: more info
The graph of is a standard exponential, not dissimilar from . This means it starts off small and quickly expands.
The graph of is a straight line with a negative gradient, for negative values of x there will be a high value of y.
Due to these properties is the only intersection