# Worksheet: Logarithmic Functions

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

**Q3: **

Rearrange the equation to find in terms of . Hence determine the inverse to the function .

- A
- B
- C
- D
- E

**Q5: **

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

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

**Q6: **

Consider the function . Find the value of .

- A
- B
- C
- D4
- E3

**Q7: **

Consider the function . Find the value of .

**Q8: **

If is the inverse of the function , find .

- A
- B
- C
- D
- E

**Q9: **

If is the inverse of the function , find .

- A
- B
- C
- D
- E

**Q10: **

Determine , given that the graph of the function passes through the point .

**Q11: **

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

**Q12: **

Given that the graph of the function passes through the point , find the value of .

- A20
- B1
- C
- D9
- E4

**Q13: **

Determine the point at which the graph of the function intersects the -axis.

- A
- B
- C
- D
- E

**Q14: **

The of a solution is given by the formula , where is the concentration of hydrogen ions. Determine the concentration of hydrogen ions in a solution whose is 8.4.

- A
- B
- C
- D

**Q15: **

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 .

**Q17: **

Use technology to plot the graphs of and . Find the coordinates where if the curves intersect, giving your answer to two decimal places.

- AThey intersect at and .
- BThe curves do not intersect.
- CThe curves are the same, so intersect everywhere.
- DThey intersect at .
- EThey intersect at .

**Q18: **

Consider the function . If , find the value of .