Final answer:
To solve the exponential equation 2³ˣ = 34, we use logarithms. Taking the logarithm base 2 of both sides of the equation, we find that x ≈ 2.8074. Therefore, the solution to the equation 2³ˣ = 34, correct to four decimal places, is x ≈ 2.8074.
Step-by-step explanation:
To solve the exponential equation 2³ˣ = 34, we need to use logarithms. Taking the logarithm base 2 of both sides of the equation, we get x = log2(34/8). Using a calculator, we find that x ≈ 2.8074. Therefore, the solution to the equation 2³ˣ = 34, correct to four decimal places, is x ≈ 2.8074.