Pre­Calculus
Lesson 3.3
Logarithmic Functions
­Now that we have had an introduction to exponential functions, we will shift our focus to the inverse relationship between exponents and logarithms. This relationship can be seen below (in 2 forms):
Graphically
Algebraically
**Algberaic Examples:
log2(32) = x
log7(x) = ­3
**Examples:
log (1/10000) = log (10­7) = log4(48) = log12 1 = **Examples:
ln e23 =
ln 32 =
*check by solving the corr. exponential expression
**Solving Simple Logarithmic Equations (Examples):
log x = 6
log x = ­2
Graphing and Analysis of Logarithmic Functions
Lesson 3.3 ­ Continued
Using previous knowledge of exponential functions,
what transformations have taken place in relation to y = log x f(x) = ­log (x + 2)
f(x) = 5 log (­x)
f(x) = ­4 log (5 ­ x) + 6
*Analyze the function, f(x) = 3 ln (2 ­ x) ­ 2 for:
domain =
range =
continuity = extrema =
symmetry =
asymptotes =
end behavior (using limits) =
Application: Measuring Sound in Decibels
­How loud (in decibels) is the human pain threshold?
­How loud (in decibels) is a jet at takeoff?
**HW Assignment ­ p. 308: 37­60 all