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- https://math.libretexts.org/Courses/Truckee_Meadows_Community_College/TMCC%3A_Precalculus_I_and_II/Under_Construction_test2_04%3A_Exponential_and_Logarithmic_Functions/Under_Construction_test2_04%3A_Exponential_and_Logarithmic_Functions_4.6%3A_Exponential_and_Logarithmic_Equations\[\begin{align*} e^{2x}-e^x&= 56\\ e^{2x}-e^x-56&= 0 \qquad &&\text{Get one side of the equation equal to zero}\\ (e^x+7)(e^x-8)&= 0 \qquad &&\text{Factor by the FOIL method}\\ e^x+7&= 0 \qquad &&\tex...\[\begin{align*} e^{2x}-e^x&= 56\\ e^{2x}-e^x-56&= 0 \qquad &&\text{Get one side of the equation equal to zero}\\ (e^x+7)(e^x-8)&= 0 \qquad &&\text{Factor by the FOIL method}\\ e^x+7&= 0 \qquad &&\text{or} \\ e^x-8&= 0 \qquad &&\text{If a product is zero, then one factor must be zero}\\ e^x&= -7 \qquad &&\text{or} \\ e^x&= 8 \qquad &&\text{Isolate the exponentials}\\ e^x&= 8 \qquad &&\text{Reject the equation in which the power equals a negative number}\\ x&= \ln8 \qquad &&\text{Solve the equat…
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_1e_(OpenStax)/04%3A_Exponential_and_Logarithmic_Functions/4.06%3A_Exponential_and_Logarithmic_EquationsUncontrolled population growth can be modeled with exponential functions. Equations resulting from those exponential functions can be solved to analyze and make predictions about exponential growth. I...Uncontrolled population growth can be modeled with exponential functions. Equations resulting from those exponential functions can be solved to analyze and make predictions about exponential growth. In this section, we will learn techniques for solving exponential functions.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_384%3A_Foundations_for_Calculus/11%3A_Exponential_and_Logarithmic_Functions/11.06%3A_Exponential_and_Logarithmic_EquationsThis section covers solving exponential and logarithmic equations using algebraic techniques, properties of exponents and logarithms, and logarithmic conversions. It explains how to apply logarithms t...This section covers solving exponential and logarithmic equations using algebraic techniques, properties of exponents and logarithms, and logarithmic conversions. It explains how to apply logarithms to isolate variables, use the one-to-one property, and handle real-world applications like exponential growth and decay. Examples illustrate step-by-step solutions for different types of equations.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_372%3A_College_Algebra_for_Calculus_(2e)/04%3A_Exponential_and_Logarithmic_Functions/4.06%3A_Exponential_and_Logarithmic_EquationsThis section covers solving exponential and logarithmic equations using algebraic techniques, properties of exponents and logarithms, and logarithmic conversions. It explains how to apply logarithms t...This section covers solving exponential and logarithmic equations using algebraic techniques, properties of exponents and logarithms, and logarithmic conversions. It explains how to apply logarithms to isolate variables, use the one-to-one property, and handle real-world applications like exponential growth and decay. Examples illustrate step-by-step solutions for different types of equations.
- https://math.libretexts.org/Courses/Quinebaug_Valley_Community_College/MAT186%3A_Pre-calculus_-_Walsh/04%3A_Exponential_and_Logarithmic_Functions/4.06%3A_Exponential_and_Logarithmic_EquationsUncontrolled population growth can be modeled with exponential functions. Equations resulting from those exponential functions can be solved to analyze and make predictions about exponential growth. I...Uncontrolled population growth can be modeled with exponential functions. Equations resulting from those exponential functions can be solved to analyze and make predictions about exponential growth. In this section, we will learn techniques for solving exponential functions.
- https://math.libretexts.org/Courses/Highline_College/Math_141%3A_Precalculus_I_(old_edition)/04%3A_Exponential_and_Logarithmic_Functions/4.06%3A_Exponential_and_Logarithmic_EquationsUncontrolled population growth can be modeled with exponential functions. Equations resulting from those exponential functions can be solved to analyze and make predictions about exponential growth. I...Uncontrolled population growth can be modeled with exponential functions. Equations resulting from those exponential functions can be solved to analyze and make predictions about exponential growth. In this section, we will learn techniques for solving exponential functions.
- https://math.libretexts.org/Courses/Mission_College/Math_001%3A_College_Algebra_(Kravets)/06%3A_Exponential_and_Logarithmic_Functions/6.06%3A_Exponential_and_Logarithmic_EquationsUncontrolled population growth can be modeled with exponential functions. Equations resulting from those exponential functions can be solved to analyze and make predictions about exponential growth. I...Uncontrolled population growth can be modeled with exponential functions. Equations resulting from those exponential functions can be solved to analyze and make predictions about exponential growth. In this section, we will learn techniques for solving exponential functions.
- https://math.libretexts.org/Workbench/Book-_Precalculus_I_for_Highline_College_w/Rational_Inequalities_and_Equations_of_Circles/1.04%3A_Exponential_and_Logarithmic_Functions/1.4.07%3A_Exponential_and_Logarithmic_EquationsUncontrolled population growth can be modeled with exponential functions. Equations resulting from those exponential functions can be solved to analyze and make predictions about exponential growth. I...Uncontrolled population growth can be modeled with exponential functions. Equations resulting from those exponential functions can be solved to analyze and make predictions about exponential growth. In this section, we will learn techniques for solving exponential functions.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_165_College_Algebra_MTH_175_Precalculus/04%3A_Exponential_and_Logarithmic_Functions/4.06%3A_Exponential_and_Logarithmic_EquationsSolve exponential equations by using a common base and the one-to-one property or rewriting in log form. Solve exponential equations that are quadratic in form. Solve log equations by using the one-to...Solve exponential equations by using a common base and the one-to-one property or rewriting in log form. Solve exponential equations that are quadratic in form. Solve log equations by using the one-to-one property or by rewriting in exponential form.
- https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/04%3A_Exponential_and_Logarithmic_Functions/4.07%3A_Exponential_and_Logarithmic_EquationsUncontrolled population growth can be modeled with exponential functions. Equations resulting from those exponential functions can be solved to analyze and make predictions about exponential growth. I...Uncontrolled population growth can be modeled with exponential functions. Equations resulting from those exponential functions can be solved to analyze and make predictions about exponential growth. In this section, we will learn techniques for solving exponential functions.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_375%3A_Pre-Calculus/13%3A_Exponential_and_Logarithmic_Functions/13.06%3A_Exponential_and_Logarithmic_EquationsThis section covers solving exponential and logarithmic equations using algebraic techniques, properties of exponents and logarithms, and logarithmic conversions. It explains how to apply logarithms t...This section covers solving exponential and logarithmic equations using algebraic techniques, properties of exponents and logarithms, and logarithmic conversions. It explains how to apply logarithms to isolate variables, use the one-to-one property, and handle real-world applications like exponential growth and decay. Examples illustrate step-by-step solutions for different types of equations.
