1. Solving Exponential Equations using Logs Wednesday, February 10, 2016 Topic 7-9 in TEXT

2. Essential Question How can I use logarithms to help me solve exponential equations?

3. Logarithms of Other Bases (Review) The calculator will not automatically evaluate logs of other bases. You have to “change the base.” The CHANGE OF BASE formula allows you to change a logarithm into any base that is needed! log b x = log a (x) / log a (b) (A log is turned into the division of the log of the value by the log of the base, with the new or desired base on the logs.) Usually we turn logs into base 10 [LOG] so we can use the calculator to evaluate them. (We can also change them into base “e” or natural base and use the [LN] button.)

4. So an expression in base 2 can be turned into an equivalent expression in any base that we need! log 2 14 can be turned into log 3 (14)/log 3 (2)… in base 3 log 2 14 can be turned into log 5 (14)/log 5 (2)… in base 5 log 2 14 can be turned into log (14)/log (2)… in base 10 If we convert it into base 10, we can evaluate it with the calculator… log 2 14 = log (14)/log (2) which is about 3.8074 All these expressions have the same value! This is usually fewer button pushes than using the [MATH] A: logBASE calculator function

5. Steps for Solving Exponential Equations 1.Isolate the power expression with the variable exponent. 2.Convert to Logarithmic form (if necessary). 3.Solve for x using linear, quadratic or evaluating skills. 4.Use the change-of-base property as needed. DO NOT round decimals until the very end! [ANS] key 5.Check for extraneous solutions.

6. Step 1: Isolate the power expression with the variable exponent (divide by 2). Step 2: Convert to Log form (base 18). Solve for x; Evaluate the log and divide by 6. Value, [STO], [“x”]

7. Step 1: Isolate the power expression with the variable exponent (add 5). Step 2: Convert to Log form (base e). Solve (add 1) & Evaluate the answer. Value, [STO], [“x”]

8. Answer: n ≈ -0.2165 20 -6n = 49 log 20 (49) = –6n log (49)/log (20) ≈ 1.299121531… = –6n n ≈ –0.2165

9. WS: Solving Exponential Equations with Logarithms (1-10) Assignment will be given in class on Friday