Final answer:
To solve the equation 56*2²ˣ = 22 for x, divide both sides by 56 and apply the logarithm base 2 to find x. Using a calculator provides an approximate value, which rounded to the nearest hundredth is x = -1.35.
Step-by-step explanation:
To solve the equation 56*2²ˣ = 22 for x, we start by isolating the exponential part of the equation. First, divide both sides of the equation by 56:
2²ˣ = rac{22}{56}
2²ˣ = 0.392857...
To remove the base 2 exponent, we apply the logarithm base 2 on both sides of the equation:
2ˣ = log2(0.392857...)
Next, we use a calculator to find the value of the right hand side:
x = log2(0.392857...)
Using a calculator, we get:
x ≈ -1.34785...
Rounding to the nearest hundredth, x = -1.35.