Final answer:
To solve the exponential equation e^(1-4x) = 2, isolate x by taking the natural logarithm of both sides. Then, rearrange the equation and solve for x using a calculator. The value of x is approximately -0.1242.
Step-by-step explanation:
To solve the exponential equation e^(1-4x) = 2, we need to isolate the variable x. Taking the natural logarithm (ln) of both sides gives ln(e^(1-4x)) = ln(2), which simplifies to (1-4x) = ln(2).
Rearranging the equation to isolate x, we have -4x = ln(2) - 1. Dividing both sides by -4 gives x = (ln(2) - 1)/-4. Using a calculator, the value of x is approximately -0.1242.