<p>Pre-Calculus/Trig 3 Name ______Logarithms Worksheet</p><p>Rewrite the exponential equation in logarithmic form. 1 1. 53 125 ______6. ______ 814  3</p><p>2 1 2. 6  ______7. 103  0 001 ______36 . 3. e3  20.085 ______8. e0  1 ______</p><p>4. e x  4 ______9. u v  w ______3 5. 82 64 ______10. ______ 9 2  27</p><p>Rewrite the logarithmic equation in exponential form. 1. log2 8  x ______6. ln143  x ______</p><p>2. log5 625  4 ______7. log1000  3 ______</p><p>3. logx 13  5 ______8. ln x  14 ______</p><p>1 1 4. log  3 ______9. 1og  2 ______2 8 100 5. log4 64  3 ______10. ln18  x ______</p><p>Use your calculator to evaluate each logarithm. Round to four decimal places.</p><p>1. log 68  ______6. ln 9548  ______</p><p>2. log100  ______7. log.0001  ______</p><p>3. ln 9  ______8. log17  ______</p><p>4. log10  ______9. ln125  ______</p><p>5. ln 216  ______10. log 6158  ______Use the change of base formula to evaluate each logarithm. Round to four decimal places.</p><p>1. log3 7  ______6. log0.5 4  ______</p><p>2. log9 0.4  ______7. log15 1250 ______</p><p>3. log7 4  ______8. log4 0.55  ______</p><p>4. 125  ______9. log1 0.015  ______log20 3 5. log6 94  ______10. log17 2  ______</p><p>Use the properties of logarithms to expand each of the following.</p><p>1. log2 5x  ______</p><p>4 2. log8 x  ______</p><p>5 3. log  ______3 x</p><p>4. ln z  ______</p><p>5. ln z(z  1)2  ______</p><p> x2 6. log7  ______y 2 z3 3  x2 1 7. log  ______ 3   x  a y 4 8. logx  ______z 4</p><p> x 9. ln  ______x2  1</p><p>10. log(x2  8x  15)  ______Use the properties of logarithms to write the following as a single logarithm.</p><p>1. ln x  ln 2  ______</p><p>2. log4 z  log4 y  ______</p><p>3. 2log2 (x  4)  ______</p><p>1 4. log 5x  ______3 3</p><p>5. log3(x  2)  log3(x  2)  ______</p><p>6. 2ln 8  5ln z  ______</p><p>7. 3ln 8  2ln y  4ln z  ______</p><p>8. 4[ln z  ln(z  5)]  2ln(z  5)  ______</p><p>9. ln x  2[ln(x  2)  ln(x  2)]  ______</p><p>3 6 3 4 10. log 5t  log t  ______2 4 4 4</p><p>Given: logx 2  0.3562 , logx 3  0.5646 , and logx 5  0.8271, Evaluate each of the following.</p><p>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  ______</p><p>5. logx 40  ______10. logx 30  ______</p>