Warm-Up: Expand .

Warm-Up: Condense .

Section 3.4 Exponential and Logarithmic Equations Objectives: You will be able to solve exponential and log equations.

*Express both sides of the equation in terms of a common base

Example 1 A. Solve 4x + 2 = 16x – 3. B. Solve .

Example 2 A. Solve 7 – 3 log 10x = 13. Round to the nearest thousandth. B. Solve log5 x 4 = 20.

*Condense each side of an equation into logarithms with the same base.

Example 3 A. Solve log2 5 = log2 10 – log2 (x – 4). B. Solve log5 (x2 + x) = log5 20.

Solving Exponential Equations Log of each side of the equation with the corresponding base.

Example 4: Solve the equation, rounding to the nearest hundredth A. 3x = 7. B. e2x + 1 = 8.

Example 5: Solve the equation, rounding to the nearest hundredth Solve 36x – 3 = 24 – 4x. Round to the nearest hundredth.

Exponential Equations in Quadratic Form Multiple exponential expressions can be solved by applying quadratic techniques Factoring Quadratic Formula Always check for extraneous solutions!!

Example 6: Solve. A. e2x – ex – 2 = 0 Round to nearest hundredth. B. e4x + e2x = 12.

Warm-Up: A. 2 ln x = 18 B. 7 – 3 log 10x = 13 C. log5 x 4 = 20 D. -3 lnx = -24

Example 7: Solve A. log x + log (x – 3) = log 28 B. ln (2x + 1) + ln (2x – 3) = 2 ln (2x – 2)

Example 8: Solve A. log (3x – 4) = 1 + log (2x + 3) B. log2(x – 6) = 3 + log2 (x – 1).

Example 9: a. This table shows the number of cell phones a new store sold in March and August of the same year. If the number of phones sold per month is increasing at an exponential rate, identify the continuous rate of growth. Then write the exponential equation to model this situation.

Example 9: b. Use your model to predict the number of months it will take for the store to sell 500 phones in one month.

Exit Slip: Solve 4x + 2 = 32 – x. Round to the nearest hundredth.