1. 4.7 (Green) Solve Exponential and Logarithmic Equations No School: Monday Logarithms Test: 1/21/10 (Thursday)

2. Vocabulary: Exponential equations are equations in which variable expressions occur as exponents. Logarithmic equations are equations that involve logarithms of variable expressions.

3. Vocabulary: Property of Equality for Exponential Equations:  If b is a positive number other than 1, then b x = b y if and only if x = y. Property of Equality for Logarithmic Equations:  If b, x, and y are positive numbers with b = 1, then log b x = log b y if and only if x = y.

4. Solve by setting exponents = to each other Solve 8 x = 4 x + 1 1. Turn equation into like bases 2. Power to a power means you multiply the exponents. 3. Set exponents = to each other since they have like bases. 4. Solve for x. 5. Check.

5. You Try: Solve 5 3x + 1 = 25 x + 1 x=1

6. Solve by taking the log of both sides Solve 8 x = 23 1. Rewrite in log form. 2. Use change of base formula to calculate.

7. You Try: Solve 4 3x = 9 x≈0.528

8. Solve using 2 Equivalent Logs Solve log 8 (x + 6) = log 8 (4 – x) 1. Prop. Of Equality of Logs 2. Solve for x. 3. Check.

9. You Try: Solve 1. log 7 (x + 2) = log 7 (2 – 3x) 2. ln(4 – 5x) = ln(x + 10) x=0 x=-1

10. Solve by creating Exponents on each side Find the solution(s) of log x + log(x + 3) = 1 1. Use Properties of Logs to condense. 2. Change to exponential form. 3. Solve for x. 4. Check.

11. You Try: Solve 1. log 6 x + log 6 (x – 5) = 2 2. 2 ln x = ln(2x – 3) + ln(x – 2) x=9 x=6