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How do I solve this equation? 5e(x-2)-5e(x)+5e(x+1)=505

I'm not quite sure about your notation. I'm going to assume 5e(x-2) = 5･exp(x-2), etc.

First, divide the eqn by 5, then you can write

exp(x)･exp(-2)-exp(x)+exp(x)･exp(1) = 101.

Factor out the exp(x), divide by its coefficient and take the natural log (ln) to get

x = ln(101)-ln(exp(2)-1+exp(1)).

Is this the right interpretation?

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