Logarithmic Functions (Section 3-2)

Essential Question: How do you use the definition of a logarithm?

Students will write a summary discussing how to use the definition of a logarithm.

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Logarithmic Function with base a f(x) = loga x ← read “log base a of x” Y = loga x if and only if x = ay

If you see a log written out without a base indicated, then a = 10

Natural Logarithmic Function: f(x) = loga x = ln x

ln x = y if and only if x = ey

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Write the logarithmic equation in exponential form. Example 1 log749 = 2

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Write the logarithmic equation in exponential form. Example 2 log5 125 = 3

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Write the logarithmic equation in exponential form. Example 3 3

64

1log4

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Write the logarithmic equation in exponential form. Example 4 ...693147.02ln

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Write the logarithmic equation in exponential form. Example 5 5ln 5 e

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Write the exponential equation in logarithmic form. Example 6 1642

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Write the exponential equation in logarithmic form. Example 7

392

1

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Write the exponential equation in logarithmic form. Example 8 ...18249.125.2 e

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Example 9 Use the calculator to evaluate f(x) = log10x at each value of x.

a. x = 10 b. x = 2.5

c. x = -2 d. x = ¼

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Evaluate the function at the indicated value of x without using a calculator. Example 9 8,log)( 2 xxxf

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Evaluate the function at the indicated value of x without using a calculator. Example 10 81,log)( 3 xxxf

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Solve the equation for x. Example 13 5loglog 88 x

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Solve the equation for x. Example 14 x2

3 3log

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Use the properties of logarithms to rewrite the expression. Example 15 x5

2 2log

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Use the properties of logarithms to rewrite the expression. Example 16

3

1log6 3

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Use the properties of logarithms to rewrite the expression. Example 17 24log99

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

Use the properties of logarithms to rewrite the expression. Example 18 4log

2

12

Essential Question: How do you use the definition of a logarithm? Students will write a summary discussing how to use the definition of a logarithm.

HW #83 pg 193-195 (1-31 odd, 33-42 all)