What is logarithmic functions

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.1: Inverse Functions
Problem 18E
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What is logarithmic functions
mmg All Righes Resaveu May m he umpral, stmed, on duplncuted, in whule ut in part. Dne in crctrouic riglus, some third party creent may be suppressed from the ellook wid'or
Functions Defined on a Cartesian Product
Define functions M: R x R- R and R: R × R -→ R × R as follows: For all ordered
pairs (a, b) of integcrs,
M(a, b) = ab and
R(a, b) zz (-a, b).
Then M is the multiplication function that sends each pair of real nuimbers to the product
of the two, and R is the reflection function that sends ench point in the plane that corre-
sponds to a pair of real numbers to the mirror image of the point across the vertical axis.
Find the following:
a. M(-1,--1)
d. R(2, 5)
b. M (. !)
e. R(-2, 5)
c. M(VZ, 2)
f. R(3,-4)
Solution
a. (-1)(-1) = |
d. (-2, 5)
b. (1/2)(1/2) = 1/4
e. (--(-2), 5) = (2, 5)
c. 2.2 = 2 ·.
f. (-3, -4)
Definition Logarithms ang Logarithmic Functioris
Let b be a positive real number with b # 1, For each positive real number x, the
logarithm' with basė b' öfi, written log, x, is the exponent to which b must be
raised to obtain x. Symbolicully.
b = X.
Jog, v =
The logarithmic function with base b'is the function from R* to R that takes each
positive réal number:x to log, x.
ItL.
pl- 7.1.8 The Logarithmic Fonction with Buse b
Find the following:
a. log, 9
b. log, )
c. logju(1)
d. log2 (2") (1m is any real number)
e. 2B2 " (n > 0)
mg An keh eden kes mul nalerially alleca de overall learning experiene. Cengage Leanting teserves the right to reimuve blitimal content al y time ubae rielas
A SHOT ON OPPO
Transcribed Image Text:mmg All Righes Resaveu May m he umpral, stmed, on duplncuted, in whule ut in part. Dne in crctrouic riglus, some third party creent may be suppressed from the ellook wid'or Functions Defined on a Cartesian Product Define functions M: R x R- R and R: R × R -→ R × R as follows: For all ordered pairs (a, b) of integcrs, M(a, b) = ab and R(a, b) zz (-a, b). Then M is the multiplication function that sends each pair of real nuimbers to the product of the two, and R is the reflection function that sends ench point in the plane that corre- sponds to a pair of real numbers to the mirror image of the point across the vertical axis. Find the following: a. M(-1,--1) d. R(2, 5) b. M (. !) e. R(-2, 5) c. M(VZ, 2) f. R(3,-4) Solution a. (-1)(-1) = | d. (-2, 5) b. (1/2)(1/2) = 1/4 e. (--(-2), 5) = (2, 5) c. 2.2 = 2 ·. f. (-3, -4) Definition Logarithms ang Logarithmic Functioris Let b be a positive real number with b # 1, For each positive real number x, the logarithm' with basė b' öfi, written log, x, is the exponent to which b must be raised to obtain x. Symbolicully. b = X. Jog, v = The logarithmic function with base b'is the function from R* to R that takes each positive réal number:x to log, x. ItL. pl- 7.1.8 The Logarithmic Fonction with Buse b Find the following: a. log, 9 b. log, ) c. logju(1) d. log2 (2") (1m is any real number) e. 2B2 " (n > 0) mg An keh eden kes mul nalerially alleca de overall learning experiene. Cengage Leanting teserves the right to reimuve blitimal content al y time ubae rielas A SHOT ON OPPO
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