Final answer:
To solve the equation 3ˣ⁺¹ = 1645, take the logarithm of both sides, isolate x, and evaluate the logarithm to find the approximate value of x.
Step-by-step explanation:
To solve the exponential equation 3ˣ⁺¹ = 1645, we need to isolate x by taking the logarithm of both sides of the equation.
Using the logarithm base 3, we have:
log₃(3ˣ⁺¹) = log₃(1645)
(x + 1)log₃(3) = log₃(1645)
Since log₃(3) = 1, the equation simplifies to:
x + 1 = log₃(1645)
To find the value of x, subtract 1 from both sides:
x = log₃(1645) - 1
Using a calculator to evaluate log₃(1645), we find:
x ≈ 4.584
Therefore, the value of x is approximately 4.584.