# Worksheet: Logarithmic Functions

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

Q1:

The function has an inverse of the form . What are the values of and ?

• A,
• B,
• C,
• D,
• E,

Q2:

Make the subject of the equation , assuming that .

• A
• B
• C
• D
• E

Q3:

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

• A
• B
• C
• D
• E

Q4:

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

• A,
• B,
• C,
• D,
• E,

Q5:

Consider the function . Find the value of .

• A
• B
• C
• D4
• E3

Q6:

Consider the function . Find the value of .

Q7:

If is the inverse of the function , find .

• A
• B
• C
• D
• E

Q8:

If is the inverse of the function , find .

• A
• B
• C
• D
• E

Q9:

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

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

Q11:

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

• A20
• B1
• C
• D9
• E4

Q12:

The pH 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

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 .

Q14:

Consider the function . If , find the value of .

Q15:

Consider the function , where is a positive real number not equal to 1. What is the domain of ?

• AAll real numbers
• B
• C
• D