# Lesson Worksheet: Logarithmic Functions Mathematics

In this worksheet, we will practice identifying, writing, and evaluating a logarithmic function as an inverse of the exponential function.

**Q4: **

The function has an inverse of the form . Determine the values of and .

- A,
- B,
- C,
- D,
- E,

**Q10: **

The magnitude of an earthquake on the Richter scale is given by , where is the intensity of the earthquake and is a fixed reference intensity. What is the approximate intensity of an earthquake with a magnitude of 4.4 on the Richter scale?

- A2,720,000 times the reference intensity
- B25,000 times the reference intensity
- C1,585 times the reference intensity
- D2,512 times the reference intensity
- E620,000 times the reference intensity

**Q13: **

The pH of a solution is given by the formula where is the concentration of hydrogen ions. Determine the pH of a solution whose concentration of hydrogen ions is .

**Q16: **

Consider the function . Find the value of .

- A3
- B
- C
- D4
- E2

**Q17: **

If is the inverse of the function , find .

- A
- B
- C
- D
- E

**Q18: **

True or False: The domain of the function is .

- ATrue
- BFalse

**Q19: **

In order to conduct a research on atherosclerosis, epithelial cells are harvested from discarded umbilical tissue and grown in the laboratory. A technician observes that a culture of nine thousand cells grows to three million cells in one week. Assuming that the cells follow the law of uninhibited growth, which states that , where is the initial number of organisms and is the constant of proportionality that satisfies the equation, find a formula for the number of cells, in thousands after days.

- A
- B
- C
- D
- E

**Q20: **

Find the range of the function .

- AAll real numbers
- B
- C
- D
- E

**Q23: **

Find the domain of the following function: .

- A
- B
- C
- D
- EAll real numbers

**Q24: **

Iodine-131 is a commonly used radioactive isotope that helps detect how well the thyroid is functioning. Suppose that the decay of iodine-131 follows the radioactive decay model, where the amount of a radioactive element at time is given by the formula , is the initial amount of the element, and is the constant of proportionality that satisfies the equation, and that the half-life (the time it takes for half of the substance to decay) of iodine-131 is approximately 8 days. If 2 grams of iodine-131 is present initially, find a function that gives the amount of iodine-131, , in grams days later.

- A
- B
- C
- D
- E

**Q25: **

One hot water pump has a noise rating of 50 decibels. One dishwasher, however, has a noise rating of 62 decibels. If it is known that the noise rating of a sound is measured in a logarithmic scale in a unit called the decibel using the formula , where is the power or intensity of the sound and is the weakest sound that the human ear can hear, how many times is the dishwasher noise more intense than the hot water pump noise? Round your answer to the nearest hundredth.