# Worksheet: Laws of Logarithms

Q1:

Calculate .

Q2:

Calculate .

Q3:

Calculate .

Q4:

Calculate .

Q5:

Find the value of without using a calculator.

Q6:

Find the value of without using a calculator.

Q7:

Determine the value of without using a calculator.

• A
• B
• C
• D
• E3

Q8:

What is the value of ?

• A
• B
• C
• D
• E

Q9:

Simplify .

Q10:

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

Q11:

Find the approximate value of , given that .

Q12:

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

Q13:

Given that and , find in terms of and .

• A
• B
• C
• D
• E

Q14:

Determine the value of without using a calculator.

Q15:

Given that , find the value of .

Q16:

Calculate .

Q17:

Find .

Q18:

Find the value of without using a calculator.

Q19:

If , what interval contains ?

• A
• B
• C
• D
• E

Q20:

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

• A0.6601
• B
• C1.1461
• D2.3502
• E4.5265

Q21:

Find the value of correct to four decimal places.

Q22:

Given that , evaluate .

Q23:

Find the value of in its simplest form.

Q24:

Find the value of without using a calculator.

Q25:

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