Solving Exponential & Logarithmic Equations 0 ln ln2 3 ln2 3

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