use a graphing calculator. solve 5.5^3x=805. round to nearest hundredth.
A. 2.91
B. 3.92
C. 1.31
D. 0.97
To solve the equation 5.5^(3x) = 805, we can take the logarithm of both sides.
Using a graphing calculator:
1. Enter the equation into the graphing calculator: 5.5^(3x) = 805.
2. Take the logarithm of both sides: log(5.5^(3x)) = log(805).
3. Simplify: (3x)log(5.5) = log(805).
4. Divide both sides by log(5.5) to isolate the variable: 3x = log(805) / log(5.5).
5. Divide both sides by 3 to solve for x: x = (log(805) / log(5.5)) / 3.
6. Use the graphing calculator to evaluate the expression on the right side of the equation.
7. Round the result to the nearest hundredth.
Calculating the result on a graphing calculator, we get:
x ≈ 3.92
Therefore, the answer to the equation is option B: 3.92 (rounded to the nearest hundredth).