4.5 - 1 Property of Logarithms If x > 0, y > 0, a > 0, and a ≠ 1, then x = y if and only if log a x = log a y.

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Presentation transcript:

Property of Logarithms If x > 0, y > 0, a > 0, and a ≠ 1, then x = y if and only if log a x = log a y.

Example 1 SOLVING AN EXPONENTIAL EQUATION Solve 7 x = 12. Give the solution to the nearest thousandth. Solution Property of logarithms Power of logarithms Divide by In 7. Use a calculator. The solution set is {1.277}.

Example 2 SOLVING AN EXPONENTIAL EQUATION Solve 3 2x – 1 =.4 x+2. Give the solution to the nearest thousandth. Solution Take natural logarithms on both sides. Property power Distributive property

Example 2 SOLVING AN EXPONENTIAL EQUATION Solve 3 2x – 1 =.4 x+2. Give the solution to the nearest thousandth. Solution Write the terms with x on one side Factor out x. Divide by 2 In 3 – In.4. Power property

Example 2 SOLVING AN EXPONENTIAL EQUATION Solve 3 2x – 1 =.4 x+2. Give the solution to the nearest thousandth. Solution Apply the exponents. Product property; Quotient property This is approximate. This is exact. The solution set is { –.236}.