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Exponential and Logarithmic Equations Section 3.4

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Objectives Solve a logarithmic equation. Solve an exponential equation.

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

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

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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

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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

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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%.

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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 11673 bacteria. Note: 11672 bacteria would also be accepted.

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How many hours will it take for there to be 10000 bacteria? The number of bacteria in a culture is modeled by where t is in hours. It will take 2.713589 hours for there to be 10000 bacteria.

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

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

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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

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

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

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

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

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

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

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

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

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

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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

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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

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

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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

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