Pre-Calculus/Trig 3

Pre-Calculus/Trig 3 Name ______Logarithms Worksheet

Rewrite the exponential equation in logarithmic form. 1 1. 53 125 ______6. ______ 814  3

2 1 2. 6  ______7. 103  0 001 ______36 . 3. e3  20.085 ______8. e0  1 ______

4. e x  4 ______9. u v  w ______3 5. 82 64 ______10. ______ 9 2  27

Rewrite the logarithmic equation in exponential form. 1. log2 8  x ______6. ln143  x ______

2. log5 625  4 ______7. log1000  3 ______

3. logx 13  5 ______8. ln x  14 ______

1 1 4. log  3 ______9. 1og  2 ______2 8 100 5. log4 64  3 ______10. ln18  x ______

Use your calculator to evaluate each logarithm. Round to four decimal places.

1. log 68  ______6. ln 9548  ______

2. log100  ______7. log.0001  ______

3. ln 9  ______8. log17  ______

4. log10  ______9. ln125  ______

5. ln 216  ______10. log 6158  ______Use the change of base formula to evaluate each logarithm. Round to four decimal places.

1. log3 7  ______6. log0.5 4  ______

2. log9 0.4  ______7. log15 1250 ______

3. log7 4  ______8. log4 0.55  ______

4. 125  ______9. log1 0.015  ______log20 3 5. log6 94  ______10. log17 2  ______

Use the properties of logarithms to expand each of the following.

1. log2 5x  ______

4 2. log8 x  ______

5 3. log  ______3 x

4. ln z  ______

5. ln z(z  1)2  ______

x2 6. log7  ______y 2 z3 3  x2 1 7. log  ______ 3   x  a y 4 8. logx  ______z 4

x 9. ln  ______x2  1

10. log(x2  8x  15)  ______Use the properties of logarithms to write the following as a single logarithm.

1. ln x  ln 2  ______

2. log4 z  log4 y  ______

3. 2log2 (x  4)  ______

1 4. log 5x  ______3 3

5. log3(x  2)  log3(x  2)  ______

6. 2ln 8  5ln z  ______

7. 3ln 8  2ln y  4ln z  ______

8. 4[ln z  ln(z  5)]  2ln(z  5)  ______

9. ln x  2[ln(x  2)  ln(x  2)]  ______

3 6 3 4 10. log 5t  log t  ______2 4 4 4

Given: logx 2  0.3562 , logx 3  0.5646 , and logx 5  0.8271, Evaluate each of the following.

1 1. log 6  ______6. log  ______x x 4 3 2. log  ______7. log 15  ______x 2 x 5 3. log 25  ______8. log  ______x x 3 4. logx 2  ______9. logx 18  ______

5. logx 40  ______10. logx 30  ______