# Finding the area of the region

find the area of the region

$$y=e^{4x}$$
$$y=e^{6x}$$

first thing i did was set them equal to each other and multiply by $$ln$$ which got me 4x=6x, that's where i got stuck. how would i find the x-intercepts?

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what do you mean? what area? function doesn't have area.....

EDIT:
These two function intersect at 1 point (0,1) only...

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find the area of the region

$$y=e^{4x}$$
$$y=e^{6x}$$

first thing i did was set them equal to each other and multiply by $$ln$$ which got me 4x=6x, that's where i got stuck. how would i find the x-intercepts?
1. You can't multiply by $ln$. Its an operator. 2. The exponential function is strictly increasing over the whole real line. There's no way it takes the same value twice (unless its of the form e^{periodic function} which it isn't in your case).
3. Drawing proper graphs for both functions referred to the same set of orthogonal axes might help. How fast do the functions grow?

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find the area of the region

$$y=e^{4x}$$
$$y=e^{6x}$$

first thing i did was set them equal to each other and multiply by $$ln$$ which got me 4x=6x, that's where i got stuck. how would i find the x-intercepts?
$$Area = \int_{x_1}^{x_2} ( e^{6x} - e^{4x} ) \delta x$$
where $$x_1$$ and $$x_2$$ should found from
$$e^{4x} = e^{6x}$$

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HallsofIvy