Final answer:
The solution to the equation ln ( x^6 ) - ln 9 = 2 is approximately 3.46. Hence, A) is correct.
Step-by-step explanation:
To solve the equation ln ( x^6 ) - ln 9 = 2, we can use the property of logarithms that states ln(a) - ln(b) = ln(a/b). Using this property, we can rewrite the equation as ln (x^6/9) = 2. To isolate the natural logarithm, we can raise both sides as a power of e, giving us x^6/9 = e^2.
To find the value of x, we can multiply both sides by 9 and then take the square root of both sides to cancel out the exponent. This gives us x^6 = 9e^2. Taking the sixth root of both sides, we have x = (9e^2)^(1/6).
Substituting the value of e as approximately 2.71828 and evaluating the expression, we get x ≈ 3.46. Rounding to the nearest hundredth, the solution is approximately 3.46.