# Worksheet: Laws of Logarithms

In this worksheet, we will practice using the laws of logarithms to simplify logarithmic expressions.

Q1:

Calculate .

Q2:

Find the value of without using a calculator.

Q3:

Simplify .

Q4:

Determine the value of without using a calculator.

• A
• B
• C3
• D
• E

Q5:

What is the value of ?

• A
• B
• C
• D
• E

Q6:

Without using a calculator, find the approximate value of given that .

Q7:

Find the approximate value of , given that .

Q8:

Given that , find, without using a calculator, the value of correct to four decimal places.

Q9:

Determine the value of without using a calculator.

Q10:

Given that , find the value of .

Q11:

Find .

Q12:

Find the value of without using a calculator.

Q13:

If , what interval contains ?

• A
• B
• C
• D
• E

Q14:

Given that and , round the value of without using a calculator.

Q15:

Find the value of correct to four decimal places.

Q16:

Find the value of without using a calculator.

Q17:

Find the value of , giving your answer in its simplest form.

Q18:

Given that and , find in terms of and .

• A
• B
• C
• D
• E

Q19:

Calculate .

Q20:

Given that , evaluate .

Q21:

Find the value of in its simplest form.

Q22:

Simplify completely.

• A
• B
• C
• D
• E

Q23:

Evaluate .

Q24:

If is any real, positive number except 1, which of the following is equal to ?

• A1
• B
• C
• D

Q25:

Is it true that ?

• Ano
• Byes