Solve 5 2x = x = 16 log 5 2x = log 16Take the common logarithm of each side. 2x log 5 = log 16Use the power property of logarithms. x = Divide each side by 2 log 5. log 16 2 log Use a calculator. Check: 5 2x (0.8614) 16 ALGEBRA 2 LESSON 8-5 Exponential and Logarithmic Equations 8-5

Use the Change of Base Formula to evaluate log Then convert log 6 12 to a logarithm in base 3. log 6 12 = Use the Change of Base Formula. log 12 log Use a calculator log 6 12 = log 3 xWrite an equation log 3 xSubstitute log 6 12 = Use the Change of Base Formula. log x log 3 ALGEBRA 2 LESSON 8-5 Exponential and Logarithmic Equations 8-5

4.589Use a calculator log 3 log xMultiply each side by log log xUse a calculator log xSimplify. x Write in exponential form. The expression log 6 12 is approximately equal to , or log ALGEBRA 2 LESSON 8-5 Exponential and Logarithmic Equations (continued) 8-5

Solve 5 2x = x = 120 log 5 5 2x = log 5 120Take the base-5 logarithm of each side. 2x = log 5 120Simplify. 2x = Use the Change of Base Formula. log 120 log 5 x 1.487Use a calculator to solve for x. ALGEBRA 2 LESSON 8-5 Exponential and Logarithmic Equations 8-5

Solve 4 3x = 1100 by graphing. The solution is x Graph the equations y = 4 3x and y = Find the point of intersection. ALGEBRA 2 LESSON 8-5 Exponential and Logarithmic Equations 8-5

The population of trout in a certain stretch of the Platte River is shown for five consecutive years in the table, where 0 represents the year If the decay rate remains constant, in the beginning of which year might at most 100 trout remain in this stretch of river? Time t01234 Pop. P(t) Step 1: Enter the data into your calculator. ALGEBRA 2 LESSON 8-5 Exponential and Logarithmic Equations 8-5 Step 2: Use the Exp Reg feature to find the exponential function that fits the data.

Step 3: Graph the function and the line y = 100. Step 4: Find the point of intersection. The solution is x 18, so there may be only 100 trout remaining in the beginning of the year ALGEBRA 2 LESSON 8-5 Exponential and Logarithmic Equations (continued) 8-5

Solve log (2x – 2) = 4. log (2x – 2) = 4 2x – 2 = 10 4 Write in exponential form. 2x – 2 = x = 5001Solve for x. log 10 4 = 4 log 10,000 4 log ( – 2) 4 Check:log (2x – 2) 4 ALGEBRA 2 LESSON 8-5 Exponential and Logarithmic Equations 8-5

Solve 3 log x – log 2 = 5. 3 log x – log 2 = 5 x32x32 Log ( ) = 5Write as a single logarithm. x32x32 = 10 5 Write in exponential form. x 3 = 2(100,000)Multiply each side by 2. x = , or about The solution is , or about ALGEBRA 2 LESSON 8-5 Exponential and Logarithmic Equations 8-5