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Warm Up1. Simplify the expressions. Leave in exponential form (no calculator!)(a) 4e-5 7e8 (b) 18e10 (c) (11e-3x)2

3e5

2. Tell whether the function is exponential growth or decay.(a) y = 2e0.6x - 1 (b) y = 5e-2x

HW Answers p. 142 #2-28 evens2. 14. 4e6

6. e3

48. 6 e10. the 3 should alsobe raised to the 2nd power(3e5x)2=32e(5x)(2)=9e10x

12. 0.22314. 5.65216. decay18. growth20. growth

22. 24.

26.

D: all real #s D: all real #sR: y > 0 R: y > 1

D: all real #sR: y > 2

28. $3450.29

questions?! Section 4.4Evaluate & Graph Logarithmic (log) Functions

Logarithm (log) - Logs are the inverses (opposite) of exponentials.

Let a & x be positive numbers and a ≠ 1.

The logarithm of x with base a is denoted by logax is defined as:

logax = y iff ay = x

Example-

52 = 25 can be written as _____________________• This expression is read "log base 5 of 25 equals 2"

log381 = 4 can be written as ___________________• This expression is read "3 to the 4th power equals 81"

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Example 1Rewrite from exponential to log form & vice versa.

LOG FORM EXP FORM

log216=4

log31=0

101=10

10-1=.1

Example 2Evaluate without a calculator.

(a) log381 (b) log5125 (c) log4256

(d) log2(1/32) (e) log416 (f) log51

(g) log164 (h) log3(-1)

General Forms

•   because ________

•   because ________

•   because ________

• Logarithms with base ______ are called common logarithms.

• Sometimes the base is assumed and not written.

• Thus, if you see a log written without a base, you assume the base is _______.

• The log button the calculator uses base _____.

Example 3Use your calculator to evaluate:(a) log 51 (b) log 4 (c) log 0.215

Example 4Solve for x.(a) logx343 = 3 (b) logx9 = 1/2

(c) 10x = 728 (d) 10x = 1/1085

remember: logs "undo" exponentials and

exponentials "undo" logs!

Natural Logarithm (ln)-

• a logarithm with base e, denoted by ln. • it is the inverse of an exponential function with base e.

logex = ln x

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Example -

e2 ≈ 7.389 can be written as _____________• This expression is read "natural log of 7.389 is approximately 2"

Example 5Rewrite as exponent or logarithm.(a) ex = 4 (b) ln 56.3 ≈ 4.03

INVERSEThe inverse of the exponential function y = 10x is y = log10x.

What do you notice?!

The inverse of the exponential function y = ex is y = lnx.

Example 6Find the inverse of the following functions.(a) y = log3x (b) y = ln(x + 1) (c) y = 5x

Essential Question:How do you evaluate &

graph logarithmic functions?

Tonight's HW:p. 147 #2-20 evens

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