Essential Question: Give examples of equations that can be solved using the properties of exponents and logarithms.

 An equation where the exponent is a variable is an exponential equation.  You solve exponential equations by converting them into logarithmic equations, and using the properties of logarithms to simplify.  As a rule: you need to get the base and exponent alone on one side of the equation first before converting to a log.

 Example ◦ Solve7 3x = 20 log 7 20 = 3xconvert to log change of base formula divide both sides by = xuse calculator round to 4 decimal places

 Example (get base/exponent alone first) ◦ Solve5 - 3 x = x = -45subtract 5 on both sides 3 x = 45divide both sides by -1 log 3 45 = xconvert to log change of base formula = xuse calculator round to 4 decimal places

 Your Turn ◦ Solve3 x = 4  ◦ Solve6 2x = 21  ◦ Solve3 x+4 = 101 

 Assignment ◦ Page 464 ◦ Problems 1 – 19 (odds) ◦ Show your work, and round your answers to 4 decimal places ◦ Ignore the directions about solving by graphing and using a table.

Essential Question: Give examples of equations that can be solved using the properties of exponents and logarithms.

 An equation that includes a logarithmic expression, such as log 3 15 = log 2 x is called a logarithmic equation.  You solve logarithmic equations by using the properties of logarithms to simplify and then converting them into exponential equations.  As a rule: you need to get the logs on one side of the equation and combined into only one log before converting to an exponential equation.  As another rule: If there is no base on a logarithmic problem, we assume the base is 10

 Example ◦ Solvelog (3x + 1) = 5Only one log? Check log 10 (3x + 1) = 5Assume base = 3x + 1Convert to exponential form 100,000 = 3x + 1Simplify left side 99,999 = 3xSubtract 1 from both sides 33,333 = xDivide both sides by 3

 Example (combining logs first) ◦ Solve2 log x – log 3 = 2 log x 2 – log 3 = 2Power rule Quotient Rule Only one log? Check Assume base = Convert to exponential form 100 = Simplify left side 300 = x 2 Multiply both sides by = xSquare root both sides

 Your Turn ◦ Solvelog (7 – 2x) = -1  ◦ Solvelog (2x – 2) = 4  ◦ Solve 3 log x – log 2 = 5  ◦ Solvelog 6 – log 3x = -2 

 Assignment ◦ Page ◦ Problems 33 – 47 (odds) ◦ Show your work, and round your answers to 4 decimal places (if necessary) ◦ Ignore the directions about solving by graphing and using a table.