Note: log 8 = log 108 and log 3 = log 103. This appears to be true, but log 5(–23) is not defined. Since the logarithm of a negative number is not defined, the only solution is x = 9. To solve an equation involving logarithms, use the properties of logarithms to write the equation in the form log b M = N and then change this to exponential form, M = b N. Gathering all terms involving the variable on one side of the equation,ĭividing both sides by 3 log 2 – 2 log 3, If you cannot, take the common logarithm of both sides of the equation and then apply property 7. To solve exponential equations, first see whether you can write both sides of the equation as powers of the same number. A logarithmic equation is an equation that involves the logarithm of an expression containing a variable. Quiz: Binomial Coefficients and the Binomial TheoremĪn exponential equation is an equation in which the variable appears in an exponent.Binomial Coefficients and the Binomial Theorem.Quiz: Definition and Examples of Sequences.Quiz: Exponential and Logarithmic Equations.Systems of Inequalities Solved Graphically.Quiz: Systems of Equations Solved Graphically.Systems of Equations Solved Graphically.Quiz: Systems of Equations Solved Algebraically.Systems of Equations Solved Algebraically.Quiz: Solving Equations in Quadratic Form.Quiz: Solving Quadratics by the Quadratic Formula.
Solving Quadratics by the Quadratic Formula.Quiz: Solving Quadratics by Completing the Square.Solving Quadratics by Completing the Square.Quiz: Solving Quadratics by the Square Root Property.Solving Quadratics by the Square Root Property.Quiz: Adding and Subtracting Radical Expressions.Adding and Subtracting Radical Expressions.Quiz: Proportion, Direct Variation, Inverse Variation, Joint Variation.Proportion, Direct Variation, Inverse Variation, Joint Variation.2x 10,000 x 5,000 We can check this answer by. The base of the log is 10, so we must raise both sides of the equation to be powers of 10: On the left hand side, the 10 and log cancel, leaving just 2x. Quiz: Adding and Subtracting Rational Expressions Get the logarithm by itself on one side of the equation.Adding and Subtracting Rational Expressions.Quiz: Trinomials of the Form ax^2 + bx + c.Quiz: Trinomials of the Form x^2 + bx + c.Quiz: Adding and Subtracting Polynomials.Quiz: Linear Equations: Solutions Using Determinants with Three Variables.Linear Equations: Solutions Using Determinants with Three Variables.Quiz: Linear Equations: Solutions Using Matrices with Three Variables.Linear Equations: Solutions Using Matrices with Three Variables.Linear Equations: Solutions Using Elimination with Three Variables.Quiz: Linear Equations: Solutions Using Elimination with Three Variables.Quiz: Linear Inequalities: Solutions Using Graphing with Two Variables.Linear Inequalities: Solutions Using Graphing with Two Variables.Quiz: Linear Equations: Solutions Using Determinants with Two Variables.Linear Equations: Solutions Using Determinants with Two Variables.Quiz: Linear Equations: Solutions Using Matrices with Two Variables.Linear Equations: Solutions Using Matrices with Two Variables.Quiz: Linear Equations: Solutions Using Elimination with Two Variables.Linear Equations: Solutions Using Elimination with Two Variables.Quiz: Linear Equations: Solutions Using Substitution with Two Variables.Linear Equations: Solutions Using Substitution with Two Variables.Quiz: Linear Equations: Solutions Using Graphing with Two Variables.
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