Worksheet Key 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Exponential and Logarithmic Equations Section 7.6 – Revised ©2013, vdang@houstonisd.org Exponential and Logarithmic Equations 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Review Exponent Equations Product: Quotient: Power: n + m n – m n* m 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Review Log Equations Product: Quotient: Power: 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Change of Base 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
CONVERT IT OUT CONVERT When in doubt . . . 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Review Convert 98 – x = 27 to Logarithmic Form 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Solving Exponential Equations If it is in exponential form, rewrite it in logarithmic form Apply the Change of Base equation Solve algebraically, Round to 3 decimal places Check 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Example 1 Solve 98 – x = 27x – 3 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Example 1 Solve 98 – x = 27x – 3 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Example 2 Solve 8x = 2x + 1 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Example 3 Solve 45x = 162x – 1 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Your Turn Solve 9x = 3x – 1 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Example 4 Solve 4x – 1 = 5 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Example 5 Solve 5x = 2 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Your Turn Solve 32x–1 = 20 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Solving Logarithmic Equations If each equation on one side shows a log: Rewrite the equation in exponential form using Isolate the variable Condense the problem Convert if necessary Solve algebraically, Round to 3 decimal places. If it is a quadratic, you may use the Quadratic Formula. List all extraneous solutions. Check 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Example 6 Solve log7(5x + 3) = 3 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Example 7 Solve log6(2x – 1) = –1 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Your Turn Solve log5(x – 2) = –1 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Example 8 Solve log4100 – log4(x + 1) = 1 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Example 9 Solve and list all extraneous solutions: log12x + log12(x + 1) = 1 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Your Turn Solve log (2x – 1) – log(x – 2) = 1 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Natural Log Equations Product: Quotient: Power: 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Example 10 Solve ln(x – 3) + ln(2x + 1) = 2 ln (x) 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Example 10 Solve ln(x – 3) + ln(2x + 1) = 2 ln (x) 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Example 10 Solve ln(x – 3) + ln(2x + 1) = 2 ln (x) 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Example 11 Solve ln(4x – 1) + ln(x + 2) = 2 ln (x) 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Your Turn Solve ln(x + 2) + ln (2x – 1) = ln x 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Example 12 Solve 5 – ln(x – 3) = ln(x – 3) 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Example 12 Solve 5 – ln(x – 3) = ln(x – 3) 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Your Turn Solve 8 – ln(2x + 1) = ln(2x + 1) 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations
Assignment Worksheet 1/2/2019 9:28 PM 7.6 - Solving Exp and Log Equations