Common Core HSF.LE.A.4 worksheet

Question 1

Solve: 2^(x − 3) = 16

x = 

Question 2

4600 is invested at 2% interest compounded continuously, A = Pe^(rt). Find A after 13 years, to 2 decimal places.

Answer 

Question 3

Use the change-of-base formula to evaluate log₇ 75 to 3 decimal places.

Answer 

Question 4

a = log x, b = log y and c = log z. Write log(x³y²/z²) in terms of a, b and c.

• A. 3a2b − 2c
• B. 3a + 2b − 2c
• C. 3a + 2b + 2c
• D. 5a − 2c

Question 5

Evaluate log₄ 16.

Answer 

Question 6

Evaluate log₆ 12 + log₆ 18.

Answer 

Question 7

Solve: log_3(x + 2) = 1. Give x as a number (fractions allowed).

Answer (as a fraction)

Question 8

Solve 5ˣ = 96. Give x to 3 decimal places.

Answer 

Question 9

Solve 9 × 2^x = 342. Give x to 3 decimal places.

Answer 

Question 10

Write 2 log 2 − log 2 + log 3 as a single logarithm log N. Find N.

Answer 

Question 11

Evaluate log_5(125) − log_5(25).

Answer 

Question 12

Solve 8^x = 4. Give a fraction or decimal.

x = 

Question 13

Solve 9^(x − 3) = 3^x.

x = 

Question 14

Solve log_b 81 = 4 for the base b.

Answer 

Question 15

Without a calculator, log₃ 109 lies between two consecutive whole numbers. What is the smaller one?

Answer 

Question 16

Evaluate log_5(125).

Answer