Solving LOG Equations and Inequalities SIMPLIFY all LOG

Solving LOG Equations and Inequalities **SIMPLIFY all LOG Expressions** CASE #1: LOG on one side and VALUE on other Side • Apply Exponential Conversion • Solve (For inequalities x < # requires 0 < x < # because of domain a) b) c) d)

Solving LOG Equations and Inequalities **Simplify all LOG Expressions** CASE #2: LOG on BOTH • Bases of both sides should be the same • Set the insides of logs equal and Solve a) b) c)

a) c) Natural Log Equations / Inequalities b) d)

Practice: Solving Logs 1. 3. 5. 2. 4.

APPLYING LOG PROPERTIES: SOLVING with PRODUCT PROPERTY [a] [b]

APPLYING LOG PROPERTIES: SOLVING with QUOTIENT PROPERTY [a] [b]

APPLYING LOG PROPERTIES: SOLVING with POWER PROPERTY [a] [b]

GENERAL PRACTICE [a] [c] [b] [d]

GENERAL PRACTICE: Continued [e] [f]

Solve Exponential Equations with Logs • Solve the exponential until form, bx = a. • Clearing Bases Using Log Conversion • Some answers cannot be evaluated by hand require calculator a) b)

Part 2: Solving Exponential Equations with Logs • Solve equation to basic exponential form b(exponent) = # • Convert to Logarithmic Form • Numerical Value = Change of Base • Solve for Variable and Use Calculator at end to get approximation a) b)

PRACTICE: Calculator Active A) B) C) D)

Example 2: Solve Base e Exponentials a) b) c) d)

Solving Exponential Equations/Inequalities with DIFFERENT bases • • a) c) Take a common log of both sides to move variables from exponents, and solve for variable. Reminder: Logs are numerical values. b) d)

(1) (3) PRACTICE: Use Common Logs to Solve (2) (4)