Question

Solve for the base in the following equation. Round to hundredths when necessary: 2ˣ⁺³=64

a) x=3.78
b) x=2.5
c) x=4
d) x=2.38

Answer 1

To solve the equation 2ˣ⁺³ = 64 for x, subtract 3 from both sides and take the logarithm using base 2. The value of x is approximately 5.93.

Step-by-step explanation:

To solve the equation 2ˣ⁺³ = 64 for x, we need to isolate the variable x. First, we can subtract 3 from both sides of the equation to get 2ˣ = 64 - 3, which simplifies to 2ˣ = 61. Next, we can take the logarithm of both sides using the base 2 logarithm. This gives us log₂(2ˣ) = log₂(61), which simplifies to x = log₂(61). Using a calculator, we find that x ≈ 5.93.