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

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

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 Method 2 Method 3 Write in exponential form Simplify and solve for x 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

CW/HW Form G