College Algebra Notes 4.3: Laws of Logarithms

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Presentation transcript:

College Algebra Notes 4.3: Laws of Logarithms Laws of Logs: Let a be a positive number, with a≠1. Let A>0, B>0, and C be any real numbers. loga(AB)=LogaA+LogaB Loga(A/B)=LogaA-LogaB Loga(AC)=ClogaA Change of Base Formula: Example 1: Rewrite using Laws of Logs. b. a. c.

College Algebra Notes 4.3: Laws of Logarithms Laws of Logs: Let a be a positive number, with a≠1. Let A>0, B>0, and C be any real numbers. loga(AB)=LogaA+LogaB Loga(A/B)=LogaA-LogaB Loga(AC)=ClogaA Change of Base Formula: Example 2: Evaluate c. a. b. Example 3: Rewrite as one log a. b.

College Algebra Notes 4.4: Exponential and Logarithmic Equations Guidelines for Solving Exponential Equations: Isolate the exponential expression on one side of the equation. Take the logarithm of each side, then use the Laws of Logarithms to “bring down the exponent.” Solve for the variable. Guidelines for Solving Logarithmic Equations: Isolate the logarithmic term on one side of the equation; you may need to 1st combine the logarithmic terms. Write the equation in exponential form (or raise the base to each side of the equation). Solve for the variable.

College Algebra Notes 4.4: Exponential and Logarithmic Equations Example 1: Find the solution to the exponential equation correct to 4dp. a. b.

College Algebra Notes 4.4: Exponential and Logarithmic Equations Example 2: Solve the equation. a. b. Not possible Not factorable so Quadratic formula Not possible

College Algebra Notes 4.4: Exponential and Logarithmic Equations Example 3: solve the logarithmic equation for x. a. b. Rewrite as an exponential Rewrite as one logarithm Rewrite as an exponential Factor & solve Check both to see if taking Log of a negative, if so exclude that value. Log of a negative doesn’t work, so only is an answer.

College Algebra Notes 4.4: Exponential and Logarithmic Equations Example 4: Invest $6500 at 6% compounded daily. a. How much money will there be after 2 years? b. How long before there is $8000 in the account?

College Algebra Notes 4.4: Exponential and Logarithmic Equations Example 5: Solve by graphing. Round to 2 dp. a. b. So: