Final answer:
To find the solution to the equation 9*8ˣ=45.68, divide both sides by 9, take the natural logarithm of both sides, and solve for x. The solution is approximately 0.82.
Step-by-step explanation:
To find the solution to the equation 9*8ˣ=45.68, we need to isolate the variable. First, divide both sides of the equation by 9 to get 8ˣ = 5.08. Then, take the natural logarithm of both sides to remove the exponent. This gives us ln(8ˣ) = ln(5.08).
Using logarithm rules, we can bring down the exponent to the front of the logarithm: x * ln(8) = ln(5.08). To solve for x, divide both sides of the equation by ln(8): x = ln(5.08) / ln(8).
Using a calculator, we can find that x ≈ 0.823909. Rounded to two decimal places, the solution to the equation 9*8ˣ=45.68 is approximately 0.82.