# Lesson Worksheet: Laws of Logarithms Mathematics

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

Q1:

Find the value of without using a calculator.

Q2:

Simplify .

Q3:

Determine the value of without using a calculator.

• A
• B
• C3
• D
• E

Q4:

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

Q5:

Find the approximate value of , given that .

Q6:

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

Q7:

Determine the value of without using a calculator.

Q8:

Find the value of without using a calculator.

Q9:

Find the value of correct to four decimal places.

Q10:

Find the value of without using a calculator.

Q11:

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

Q12:

Given that and , find in terms of and .

• A
• B
• C
• D
• E

Q13:

Find the value of in its simplest form.

Q14:

Simplify completely.

• A
• B
• C
• D
• E

Q15:

Evaluate .

Q16:

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

• A1
• B
• C
• D

Q17:

Is it true that ?

• ANo
• BYes

Q18:

Is it true that ?

• ANo
• BYes

Q19:

Is it true that ?

• ANo
• BYes

Q20:

Find the value of without using a calculator.

Q21:

Which of the following is equal to ?

• A
• B
• C
• D
• E

Q22:

Determine the value of without using a calculator.

Q23:

Ethan and Elizabeth were both asked to solve the equation by taking logarithms. Ethan used base 10 logarithms, while Elizabeth used the natural logarithm. When they compared results, what did they discover?

• A
• B
• C
• D
• E

Q24:

Find the perimeter of the figure below. Q25:

Find the value of without using a calculator.