6. 3 Logarithmic Functions Objectives: Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic functions to solve equations. Standard: S. Analyze properties and relationships of functions. Lesson 6.3: Logarithmic Functions

Warm Up:

Logarithms are used to find unknown exponents in exponential models. Logarithmic Functions define many measurement scales in the sciences, including the pH, decibel, and Richter scales.

With logarithms, you can write an exponential equation in an equivalent logarithmic form.

You can evaluate logarithms that have a base of 10 by using the key on a calculator. log

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The inverse of the exponential function y = 10 x is x = 10 y. To rewrite x = 10 y in terms of y, use the equivalent logarithmic form, y = log 10 x.

The logarithmic function y = log x with base b, or x = b y, is the inverse of the exponential function y = b x, where b ≠ 1 and b > 0. One-to-one Property of Exponents If b x = b y, then x = y.

“TRY THIS” top 373 a. v = 3 b. v = 5 c. v = 729

The function is used in chemistry to measure pH levels. The pH of a solution describes its acidity. Substances that are more acidic have a lower pH, while substances that are less acidic, or basic, have a higher pH. The pH of a substance is defined as pH = -log 10 [H + ], where [H + ] is the hydrogen ion concentration of a solution in moles per liter.

Try These: p. 374 #8 - 11

Homework: Practice 6.3 Quiz on Lessons 6.1 – 6.4 This Friday