Focus: 1. Recognize and evaluate logarithmic functions. Use logarithmic functions to solve problems.

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Presentation transcript:

Focus: 1. Recognize and evaluate logarithmic functions. Use logarithmic functions to solve problems

Logarithmic functions are widely used in measurement scales such as the pH scale with ranges from 0 to 14

 Logarithms are used to find unknown exponents in exponential models  How many years will it take to double your money when invested at 5%? - Does the initial investment matter? - Does compounding matter?

 For any positive base b, where b ≠ 1

 A logarithm with a base of 10 is called a common logarithm. If no base is written for a logarithm, the base is assumed to be 10. for example…  You can use mental math to evaluate some logarithms.

 A logarithm with a base of e is called a natural logarithm and is abbreviated as “ln” (rather than ). Natural logarithms have the same properties as log base 10 and logarithms with other bases.

 Write in logarithmic form  Write in exponential form  You can evaluate logarithms with a base of 10 by using the “log” key on a calculator Exponential Form Logarithmic Form

 Solve for x: Round your answer to the nearest thousandth.  Solve for x: Round your answer to the nearest thousandth.

Convert to logarithmic form Convert to exponential form we write as

Evaluate each logarithm. We must get same bases Base Must write 64 as a power of base 4, so, what to the power of 4 will give 64? 4 to the 3 rd power gives 64 According to the log property, since we have same bases, the answer is the exponent, 3

 Evaluate each logarithm

 In Class Wkst 4.3  Homework:  4.3, p. 253: 2-14