Exponential and Logarithmic Equations Section 3.4.

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Presentation transcript:

Exponential and Logarithmic Equations Section 3.4

Objectives Solve a logarithmic equation. Solve an exponential equation.

Solve the equation OR Take the logarithm of both sides of the equation Change to logarithmic form

Solve the equation OR Change to logarithmic form Take the logarithm of both sides of the equation

Solve the equation Change to logarithmic form OR Take the logarithm of both sides of the equation OR negative numbers are not in the domain of a logarithm Solve using factoring

Solve the equation Change to logarithmic form OR Take the logarithm of both sides of the equation OR negative numbers are not in the domain of a logarithm Solve using the quadratic formula

What is the initial number of bacteria? What is the relative growth rate of the bacterium population The number of bacteria in a culture is modeled by where t is in hours. Initial population is 2310 bacteria. The relative growth rate is.54 or 54%.

How many bacteria will there be in three hours? The number of bacteria in a culture is modeled by where t is in hours. The population in three hours will be bacteria. Note: bacteria would also be accepted.

How many hours will it take for there to be bacteria? The number of bacteria in a culture is modeled by where t is in hours. It will take hours for there to be bacteria.

Solve the equation Change to exponential form OR Exponentiate both sides of the equation

Solve the equation Change to exponential form OR Exponentiate both sides of the equation

Solve the equation Check possible solutions in original equation Continued negative numbers are not in the domain of a logarithm arguments are both positive only solution is

Solve the equation Change to exponential form Exponentiate both sides of the equation OR Factoring Check answers in original equation Both answers are good.

Solve the equation Change to exponential form Exponentiate both sides of the equation Quadratic Formula OR

Solve the equation Quadratic Formula Check answers in original equation Both answers are good. Continued

Solve the equation 0 is not in the domain of a logarithm only solutions are

Solve the equation Change to logarithmic form We will assume that the left side is the exponential function change of base

Solve the equation Change to logarithmic form We will assume that the right side is the exponential function change of base

Solve the equation Take the logarithm of both sides of the equation

Solve the equation OR Change to logarithmic form Take the logarithm of both sides of the equation change of base

Solve the equation Move all logarithms to one side and combine using the Laws of Logarithms

Solve the equation Change to logarithmic form Take the logarithm of both sides of the equation Move all logarithms to one side and combine using the Laws of Logarithms - Continued OR

Solve the equation Check answers in original equation Move all logarithms to one side and combine using the Laws of Logarithms - Continued 0 is not in the domain of a logarithm only valid answer is x = 32

Solve the equation Combine logarithms to have a single logarithm on each side Exponentiate both sides of the equation

Solve the equation Combine logarithms to have a single logarithm on each side – Continued Check answers in original equation 0 is not in the domain of a logarithm only valid answer is x = 32