Properties of Logarithms

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Presentation transcript:

Properties of Logarithms Section 11.4 Properties of Logarithms

For a > 0, b > 0, b ≠ 1, the equations are equivalent. Exponential/Logarithmic Forms Property Definition Introduction Property For a > 0, b > 0, b ≠ 1, the equations are equivalent.

Exponential/Logarithmic Forms Property Solving Equations in Logarithmic Form Example Solve for x. 1. 2. Solution

Exponential/Logarithmic Forms Property Solving Logarithmic Equations in One Variable Example 1. Solution

Exponential/Logarithmic Forms Property Solving Logarithmic Equations in One Variable Solution Continued 2.

Power Property for Logarithms Power Property for Logarithms and of Equality Property For x > 0, b > 0 and, b ≠ 1 In words: A logarithm of a power of x is the exponent times the logarithm of x. For positive real numbers a, b, and c where b ≠ 1, the equations are equivalent. Property

Solve the equation Check solution: Power Property for Logarithms Solving an Exponential Equation Example Solve the equation Check solution: Solution

Power Property for Logarithms Solving an Exponential Equation Warning Watch parenthesis:

Power Property for Logarithms Solving an Exponential Equation Example Solve Solution

Power Property for Logarithms Solving an Exponential Equation Solution Continued Check solution:

Power Property for Logarithms Solving an Exponential Equation Warning That is why we began by dividing both sides by 3. To solve some equations of the form abx = c for x, we divide both sides of the equation by a, and then take the log of both sides. Next we use the power property of logarithms.

Power Property for Logarithms Solving an Exponential Equation Example Solve Solution

Check solution with graphing calculator: Power Property for Logarithms Solving an Exponential Equation Solution Continued Check solution with graphing calculator:

Power Property for Logarithms Solving an Exponential Equation Example Solve Solution

Solving Equations in One Variable by Using Graphs Using Graphs to Solve Equations in One Variable Example Use a graph to solve Use the “intersect” feature to find the solution to the system . Solution