Solving two graphs

Nov 2009
6
0
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.
 
Last edited:

e^(i*pi)

MHF Hall of Honor
Feb 2009
3,053
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West Midlands, England
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 \(\displaystyle (1,3)\) is a point of intersection


Edit: more info

The graph of \(\displaystyle y=3^x\) is a standard exponential, not dissimilar from \(\displaystyle e^x\). This means it starts off small and quickly expands.

The graph of \(\displaystyle y=5-2x\) 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 \(\displaystyle (1,3)\) is the only intersection
 
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