Final answer:
To solve 5e³ʸ = 33, divide by 5 and apply the natural logarithm to both sides, then solve for x. Rounded to the nearest tenth, the value of x is 0.7. The correct answer is option a.
Step-by-step explanation:
To solve the equation 5e³ʸ = 33 and find the value of x that makes the equation true, we first divide both sides of the equation by 5 to isolate the exponential expression. This gives us e³ʸ = 33 / 5. Next, we compute the right-hand side to get e³ʸ = 6.6.
Now, we apply the natural logarithm (ln) to both sides of the equation because the natural logarithm is the inverse operation of the exponential function with base e. This yields 3x = ln(6.6). To solve for x, we divide both sides by 3, resulting in x = ln(6.6) / 3.
Using a calculator, we find the natural logarithm of 6.6 and then divide by 3, which gives us the approximate value of x. Rounded to the nearest tenth, the solution to x is 0.7, which corresponds to option a.