Final answer:
To solve for x in the given equations, one must apply the inverse operations: cube root for x³, base 10 exponential for log(x), natural log for e^x, and log base 3 for 3^x. The equation x=9 does not require an inverse operation.
Step-by-step explanation:
To match the given equations with the correct INVERSE function that should be applied to solve the equation for x, consider the property that inverse functions 'undo' each other. The answers are based on understanding this principle.
- a) x³= 27: Here, we need to 'undo' the cube of x. The inverse operation of cubing a number is taking the cube root. Answer: B. Cube root
- b) log(x)=4.9: The inverse operation to a logarithm is an exponential function. Here, we're dealing with a common log (base 10), so the inverse is the base 10 exponential. Answer: C. Base 10 Exponential
- c) e^x=13.6: To 'undo' an exponential function with base e, we use the natural log (ln). Answer: D. Natural Log
- d) x=9: This equation doesn't require an inverse operation as x is already isolated. No INVERSE function is necessary.
- e) 3^x=81: The base of the exponential function is 3, and to 'undo' this, we can apply a logarithm with the same base, which is log base 3. Answer: A. Log Base 3
The answers are: a) B, b) C, c) D, d) None, e) A.