Solve Exponential Equations Today’s Objectives: Review how to solve exponential equations that do not require logarithms. Solve exponential equations that require logarithms.

Type 1: Solve exponential equations without logarithms (review 7.2) If bx = by, then x=y for b≠1. If two powers with the same base are equal, then their exponents are equal.

Type 1: Solve exponential equations without logarithms 43x = 8x+1 Steps: 1. Rewrite both sides of the equation with the same base 2. Set the exponents equal to one another. 3. Solve for x 4. Check your solution

Type 1: Solve exponential equations without logarithms (review 7.2) 812x= 27x-1/9x Steps: 1. Rewrite both sides of the equation with the same base 2. Set the exponents equal to one another. 3. Solve for x 4. Check your solution

Your turn! Complete these on your whiteboard/w partner

Evaluate the following logarithms: What if I can’t write both sides using the same base???? We will rewrite the equation using logarithms Evaluate the following logarithms:

Type 2: Solve exponential equations with logarithms Steps: Isolate the base with the variable exponent on one side of the equal sign. Take the log with the same base of each side Solve for x. Use change of base property, if needed. Check for extraneous solutions. 102x-3+4 = 21

Type 2: Solve exponential equations with logarithms Steps: Isolate the base with the variable exponent on one side of the equal sign. Take the log with the same base of each side Solve for x. Use change of base property, if needed. Check for extraneous solutions. ½ex+2 + 3 = 25

Your turn! Complete these on your whiteboard/w partner –3e-x – 4 = –13

Now, we can solve this algebraically! Suppose you deposit $5000 into a bank account that receives 2.4% interest monthly. How many years will it take for your account to reach $10,000? Now, we can solve this algebraically!

Complete these on the whiteboards with your partner! Your turn! Complete these on the whiteboards with your partner! Suppose you deposit $2,000 into a bank account where the interest is compounded continuously with an interest rate of 5%. When will your bank account have a balance of $8,000? In 1990, Euler Town had a population of 30,000. If the population decreases by 10% each year, during which year will the population be 10,000?

Solve Logarithmic Equations Today’s Objectives Solve logarithmic equations with the same base. Solve logarithmic equations by rewriting in exponential form.

Answers to Last Night’s Homework  

Answers to Last Night’s Homework  

Type 1: Solve logarithmic equations with same base Type 3: Solve logarithmic equations with the same base If logbx = logby, then x = y.

Type 3: Solve logarithmic equations with the same base Steps: If the logarithms have the same base, then drop the logarithms. Solve for x Check your solution. log3(5x-1) = log3(x+7) 5x – 1 = x + 7 5x = x + 8 4x = 8 x = 2

Type 3: Solve logarithmic equations with the same base Steps: If the logarithms have the same base, then drop the logarithms. Solve for x Check your solution. log4(x2-16) - log4(2x-1)=0

Type 4: Solve equations with one logarithm Steps: Isolate the logarithm. Rewrite in exponential form. Solve for x. Check for extraneous solutions. 5log5(3x + 1) + 3 = 13 5log5(3x + 1) = 10 log5(3x + 1) = 2 3x + 1 = 52 3x + 1 = 25 3x = 24 x = 8

Type 4: Solve equations with one logarithm Steps: Isolate the logarithm. Rewrite in exponential form. Solve for x. Check for extraneous solutions.

Your turn! Complete these on your own 1. 7log9(x + 8) - 2 = 5 2. 9 + log3(x + 3) = 9 3. log3(9x)2 = 8 4. 5+ln(x+1)1/2=6 1 2) -2 3) 9 4) 6.39

Type 5: Solve equations with 2+ logarithms log5x + log(x-1)=2 Steps: Isolate the logarithms on one side of the equation. Use properties of logarithms to condense. Rewrite in exponential form. Check for extraneous solutions.

Type 5: Solve equations with 2+ logarithms log5x + log(x-1)=2 Steps: Isolate the logarithms on one side of the equation. Use properties of logarithms to condense. Rewrite in exponential form. Check for extraneous solutions. log (5x) + log(x-1) = 2 log (5x)(x-1) = 2 log (5x2 – 5x) = 2 10log(5x -5x) = 102 5x2 - 5x = 100 x2 – x – 20 = 0 (x – 5)(x + 4) = 0 x = 5, x = –4

Your turn! Complete these on your own 1. log 7 =2 - log x 2. log72 – log7(x-5) = 2 3. ln x + ln(7) = 3 4. 3log2x - log2(2x) = 3 1) 100/7 2) 3) 4)

EXIT CARD Homework: Solving Logarithmic Equations Worksheet

Day 3: “Speed Dating Exp/Log Equations” Activity Students will sit next to the student with the same numbered card. Students will become the “master” of the problem they are given. Students can check their solution on the back of their card and work together with their partner. After all students have the solution to their problem, they will switch seats similar to speed dating. They will write down their new partner’s problem on their paper and solve it. If students have difficulty, they will ask their partner how to “master” the question. Students will switch after a given amount of time.