Answer:
x = ln(4) ≈ 1.3862944
Explanation:
You apparently want the solution to the equation 2e^(2x) -2e^x -24 = 0.
Solution
This is effectively a quadratic in e^x. Dividing by 2, we get ...
(e^x)^2 -(e^x) -12 = 0
Factoring gives ...
((e^x) -4)((e^x) +3) = 0
Solutions will be the values of x that make the factors zero.
e^x -4 = 0 ⇒ e^x = 4 ⇒ x = ln(4)
e^x +3 = 0 ⇒ e^x = -3 ⇒ x = ln(-3) . . . . not defined for real numbers
The only real solution is x = ln(4) ≈ 1.3862944.
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Additional comment
In the complex numbers, the other solution is x = ln(-3) = ln(3) +πi.