Solve
𝑒
(
1
−
2
𝑥
)
=
4
for
𝑥
.

Question

Solve 
𝑒
(
1
−
2
𝑥
)
=
4
  for 
𝑥
.

BlackTom AI · Accepted Answer

The problem asks us to solve the equation e^(1 - 2x) = 4 for x.

First, take the natural logarithm of both sides to remove the exponential:
1 - 2x = ln(4).

Next, solve for x by isolating it:
-2x = ln(4) - 1,
so x = (1 - ln(4)) / 2.

Now, let's rewrite (1 - ln(4)) / 2 in an alternative equivalent form to match the provided expression. Distributing the denominator gives x = -(1/2)[ln(4) - 1]. Since ln(4) - 1 = -1 + ln(4), this becomes x = -(1/2)[-1 + ln(4)].

Regarding the answer options: the original prompt lists options, but in the provided data there are no explicit multiple-choice options returned. The solitary answer value given corresponds to the algebraic form x = -(1/2)[-1 + ln(4)], which is algebraically equivalent to x = (1 - ln(4)) / 2.

If you were evaluating a multiple-choice set, you would compare each option to the derived expression. Any option that equals (1 - ln(4)) / 2, or equivalently -(1/2)[-1 + ln(4)], would be correct, while options that do not equal this value would be incorrect. In this scenario, since no alternative choices are presented, there isn’t another option to contrast against.

MATH-112-301-001 Unproctored Midcourse 1 Practice Exam 2

Solve 𝑒 ( 1 − 2 𝑥 ) = 4 for 𝑥 .

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