1. ## Solving two graphs

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.

2. Originally Posted by ConMan
3^x = -2x+5
Cannot be solved using algebra. Numerical solving required...

3. Originally Posted by ConMan
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 $(1,3)$ is a point of intersection

The graph of $y=3^x$ is a standard exponential, not dissimilar from $e^x$. This means it starts off small and quickly expands.
The graph of $y=5-2x$ 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 $(1,3)$ is the only intersection