Exponential and Logarithmic Equations What you ‘ll learn To solve exponential and logarithmic equations Vocabulary Exponential equation, Logarithmic equation

Take note: Any equation that contains the form ,such as where the exponent includes a variable, is an exponential equation. Problem 1: What is the solution of ? Rewrite the terms with a common base Power Property of Exponents If two numbers with the same base are equal then the exponents have to be equal Solve and simplify Your turn

Solving an Exponential Equation- Different Base Problem 2:What is the solution of ? Take the logarithm of each side Power Property of Logarithms Divide each side by to isolate the x, then by 3 Check your answer Your turn Answer:

Problem 3: What is the solution of ? Method 1 Method 2 Solving an Exponential Equation with a Graph or Table Problem 3: What is the solution of ? Method 1 Method 2 Solve using a graph Solve using a table Using a graphing calculator Enter Use table setup and to locate the x- value that gives you the y-value closest to 6000 Adjust the window that you can find the point of intersection Your turn Answer:

Method 1 Method 2 Remember to add the note to set up graphing calculator

Modeling with an Exponential Equation. Problem 4: Wood is a sustainable, renewable, natural resource when you manage forest properly. Your lumber company has 1,200,000 trees. You plan to harvest 7% of the tree each year. How many years will it take to harvest half of the trees? Know Need Plan Number of trees Number of years it takes to Write an exponential equation Rate of decay harvest 600,000 trees Use log to solve the equation. Step 1: Is an exponential model reasonable for this situation? Yes, you are harvesting a fixed percentage each year. Step 2: Define the variables and determine the model n: the number of year it takes to harvest half of the tree. T(n): the number of trees remaining after n years.

Step 3: Use the model to write an exponential equation A reasonable model is Step 3: Use the model to write an exponential equation Step 4: Solve the equation. Use log Isolate the term with n Take logarithm of each side Power property of Logarithm Solve for n Use a calculator It will take about 9.55 years to harvest half of the original trees

Your turn: After how many years will you have harvested half of the trees if you harvest 5% instead of 7% yearly. Answer Take a note: A logarithmic equation is an equation that includes one more logarithms involving a variable.

Problem 5: Solving a Logarithm Equations. Method 1 Write in exponential form Simplify and solve for x Method 3 Method 2 Answer: 1.45

Using logarithmic Properties to Solve an Equation Problem 6 What is the solution of Product Property of Logarithm Write in exponential form Simplify to a quadratic equation in standard form Factor the trinomial Solve for x Check

Your turn: What is the solution of Answer: 200

Classwork odd Homework even TB pgs. 473-474 exercises 7-78