Practice with Logarithmic Expressions Topic Index | Algebra2/Trig Index | Regents Exam Prep Center

Choose the best answer for each question.
You will need a calculator for certain questions.
(If not specified, round answer to the nearest thousandth.)

 1. Write in logarithmic form. Choose: Explanation Remember that logs yield exponents.

 2. Solve for x: Choose: 10 25 32 Explanation Write in equivalent exponential form. 5^2 = x x = 25

 3. Calculate: Choose: 2.369 4.966  5.455 Explanation Remember to use the change of base formula to enter this expression into your calculator. log(234)/log(3)

 4. Calculate: Choose: 1 2  10 Explanation log 100 = 2 log 10 = 1 log(100)/log(10)=2/1=2

 5. Calculate: Choose: 1 2/3 Explanation log (base 3) 9 = 2 log (base 2) 8 = 3 Ans: 2/3

 6. Using the properties of logs, write in expanded form: Choose:

 7. Using the properties of logs, write in expanded form: Choose:

 8. Using the properties of logs, write in expanded form: Choose:

 9. Express as a single logarithm:                          Choose:

 10. Express as a single logarithm:         Choose:

 11. Solve for x Choose: 3 9 27

 12. Given: find a.)  ln 8        b.)        c.) Please do NOT use your calculator for this problem!!! Choose for a: 0.333  0.960498 2.079 Choose for b: 0.3465 0.8325 1.1772 Choose for c: -2.079 -4.158 -5.544 Explanation a.) ln 8 = ln (2•4) = ln 2 + ln 4 = .693 + 1.386 b.) ln 2^(1/2) = (1/2) ln 2 = (1/2)•.693 c.) ln(1/64) = ln(4^-3) = -3 ln 4 = -3 • 1.386 Different solution methods are possible, but the answers remain the same.

 13. Given:      find  . Choose: 3.342 4.295 6.684

 14. True or False: Choose: True False Explanation Let's look at each piece separately first: log base b of b^10 = 10 log base b of b Now, log base b of b --> b^x = b which gives a result of 1. So, 10 • 1 = 10 Now, the term being subtracted: log base b of 1 --> b^x = 1 which tells us the result is 0. So together we have 10 - 0 = 10. TRUE

 Topic Index | Algebra2/Trig Index | Regents Exam Prep Center Created by Donna Roberts