# Solving two graphs

#### 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.

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#### Wilmer

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

#### e^(i*pi)

MHF Hall of Honor
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

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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#### ConMan

Thank you for your timely help. (Nod)