Solving a Logarithmic Equation - Concept

Concept Concept (1)

Just as we can use logarithms to access exponents in exponential equations, we can use exponentiation to access the insides of a logarithm. Solving logarithmic equations often involves exponentiating logarithms in order to get rid of the log and access its insides. Sometimes we can use the product rule, the quotient rule, or the power rule of logarithms to help us with solving logarithmic equations.

Sample Sample Problems (6)

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Solving a Logarithmic Equation - Problem 1

Solve:

log3(x² + 10x + 25) = 4
Problem 1
How to solve a logarithmic equation of a trinomial by putting it into exponential form and factoring.
Solving a Logarithmic Equation - Problem 2

Solve:

2log4(3x − 2) = 6
Problem 2
How to solve a logarithmic equation of a binomial by putting it into exponential form.
Solving a Logarithmic Equation - Problem 3

Solve:

log7(5 − x) = log78
Problem 3
How to solve a logarithmic equation with a single logarithm on both sides of the equal sign.
Solving a Logarithmic Equation - Problem 4
Problem 4
The connection between algebraic extraneous solutions to logarithmic equations.
Solving a Logarithmic Equation - Problem 5
Problem 5
Using the property that if log x = log y, then x = y , and checking for extraneous solutions.
Solving a Logarithmic Equation - Problem 6
Problem 6
How to solve an equation of the form log x = constant