3^√1-x = 2

To solve the equation 3^√(1-x) = 2, we need to isolate the variable x.

First, let's get rid of the exponent by taking the logarithm of both sides of the equation. Since the base is 3 on the left side, we'll take the logarithm base 3 of both sides:

log₃(3^√(1-x)) = log₃(2)

Using the property of logarithms, we can bring the exponent down:

√(1-x) * log₃(3) = log₃(2)

Since log₃(3) simplifies to 1, the equation becomes:

√(1-x) = log₃(2)

Next, square both sides of the equation to eliminate the square root:

(√(1-x))² = (log₃(2))²

1-x = (log₃(2))²

Now, solve for x by isolating it on one side of the equation:

1 - (log₃(2))² = x

You can further simplify the equation as needed, depending on the required level of precision.