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What is logarithmic functions

What is logarithmic functions

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 22E: A relation R on a nonempty set A is called asymmetric if, for x and y in A, xRy implies yRx. Which...
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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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