# Worksheet: Evaluating Logarithms with Different Bases

In this worksheet, we will practice expressing an exponential equation in logarithmic form, and vice versa, and how to evaluate logarithms with various bases.

Q1:

Express in its equivalent logarithmic form.

• A
• B
• C
• D

Q2:

What is the value of ?

• A1
• B
• C8
• D2
• E4

Q3:

Find .

Q4:

If , what is the value of ?

• A8
• B
• C
• D
• E

Q5:

Find the solution set of the equation in .

• A
• B
• C
• D

Q6:

Find the solution set of the equation in .

• A
• B
• C
• D
• E

Q7:

Find the value of correct to 4 decimal places.

Q8:

Use a calculator to find the number of digits of the number .

Q9:

Triangle is right-angled at . Find its area, given that and .

Q10:

Find the values of and respectively.

• A1 , 2
• B3, 1
• C1 , 1
• D3, 2
• E2, 2

Q11:

Use a calculator to find the value of . Give your answer correct to four decimal places.

Q12:

Since , what can we conclude about ?

• A is less than 2.
• B is more than .
• C is more than 1.
• D is less than .
• E is less than .

Q13:

Find the value of correct to 4 decimal places.

Q14:

Given that and , find the value of . Give your answer correct to four decimal places.

Q15:

Given that , evaluate .

Q16:

Simplify .

• A2
• B
• C10
• D

Q17:

Find the value of the number shown with the dot on the given logarithmic scale. Round your answer to the nearest thousandth.

Q18:

What is the value of ?

• A
• B
• C5
• D
• E

Q19:

What is the value of ?

Q20:

What is the value of ?

• A
• B
• C12
• D
• E