e^x times e^(x+1) =1.
Combine exponential expressions to make a single exponential expresison.
Then convert to logarithm. then solve.
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So, when combining powers, so long as the base of the two powers are the same, we can combine them by simply adding the powers together.
So e^(x) * e^(x+1) can be combined to become e^(2x+1).
Now we have a single exponential equal to a constant. e^(2x+1) = 1
We can apply the natural logarithm to both side of the equation. ln( e^(2x+1) ) = ln(1)
e is the base of natural log, so when you take the natural log of an exponential the two cancel each other out and you are left with whatever was in the power of the exponential.
ln( e^(2x+1) ) becomes 2x+1.
On the other side of the equation we have the natural log of one, which is just zero, so ln(1) = 0. Therefore our whole equation becomes:
2x+1 = 0
Now it's just a simple case of solving for x.
2x = -1
x = -1/2
And there is our final answer. I hope this solution helped you.
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