# 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:

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

• Aall real numbers
• B
• C
• D

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 .

Q16:

The formula for calculating the magnitude of an earthquake is . One earthquake has magnitude of 3.9 on the MMS scale. If a second earthquake has 750 times as much energy as the first, find the magnitude of the second one. Round the answer to the nearest hundredth.

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 .