Solving Exponential & Logarithmic Equations 0 ln ln2 3 ln2 3

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$Math 120 Final Exam Review$

$Math 120 Final Review: Multiple Choice Version 1$

Example 3:Solve the exponential equations.a. 2 7 b. 4 9 c. 2 10Solutions:Method 1: Method 2:a. 2 7 Original Equationa. 2 7 Original Equationlog 2 log 7 Take the logarithm of both sideslog 2 log 7 Take the logarithm of both sideslog 2 log 7 Property of Logarithms log 7 Inverse Property 2.807 Solve for 2.807 Change of Base Formula Method 1: Method 2:b. 4 9 Original Equationb. 4 9 Original Equation 3 3 4.585 Solve for log 4 log 9 Take the logarithm of both sideslog 4 log 9 Take the logarithm of both sides 3 log 4 log 9 Property of Logarithms 3 log 9 Inverse Property 3 Divide both sides by log 4 3 Change of Base Formulac. 2 10 Original Equation 5 Divide both sides by 2ln ln 5 Take the logarithm of both sides ln 5 1.609 Inverse PropertyExample 4:Solve 2 log 5.Solution:2 log 5 Original Equationlog Divide both sides by 24 ⁄ Change to exponential form 32Example 6:Solve 20 ln 0.2 30.Solution:Simplify20 ln 0.2 30 Original Equationln 0.2 1.5 Divide both sides by 200.2 . Change to exponential form 5 . 22.408 Divide both sides by 0.2Example 5:Solve 3 log 6.Solution:3 log 6 Original Equationlog 2 Divide both sides by 310 Change to exponential form 100SimplifyExample 7: Solving a Logarithmic Equationusing ExponentiationSolve log 2 log 3 1Solution:log 2 log 3 1 Original Equationlog 1 Condense the left side3 3 Exponentiate both sides 3Inverse Property2 3 9 Multiply both sides by 3 9Solve for
Practice ProblemsSolve the following equations:Remember that the arguments of all logarithms must be greater than 0. Also exponentials in the form of will be greater than 0. Be sure to check all your answers in the original equation.1. 3 812. 8 43. 54. 14 3 115. 6 ln 3 06. log3 1 27. ln ln 3 48. 2 ln 3 49. 5 410. ln 2 611. 4 0.2512. 2 5 3 013. log 3 log log 3214. 2 log 4 015. log log 3 216. log 5 log 2 317. 4 ln2 3 1118. log log 6 2 log 419. 2 6420. 5 2521. 4 22. 3 8123. log 524. log 325. log 2 log 10026. ln 4 ln 727. log 2 1 228. log 10 229. 3 50030. 8 100031. ln 7.2532. ln 0.533. 2 . 4534. 100 . 2035. 121 4 1836. 251 1237. log 2 1.538. log 2 0.6539. log 5 740. 4 log 1 4.841. log log 3 342. 2 log log 1 1
Page 1: Solving Exponential & Logarithmic E

Solving Exponential & Logarithmic Equations 0 ln ln2 3 ln2 3

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