Please write it on paper. 13. Recall from Section 2.1 that the set of positive realnumbers R+ is a vector space under the "addi-tion" x y = xy and the "scalar multiplication"cox=xc.a) Show that the natural logarithm is a lineartransformation from R+ to R.b) Show that the exponential function is a linear dtransformation from R to R+.

To answer the question we use the properties of natural logarithm and exponential functions and use…

13. Recall from Section 2.1 that the set of positive real numbers R+ is a vector space under the "addi- tion" x y = xy and the "scalar multiplication" cox=xc. TOPSTO a) Show that the natural logarithm is a linear transformation from R+ to R. b) Show that the exponential function is a linear transformation from R to R+.

13. Recall from Section 2.1 that the set of positive real numbers R+ is a vector space under the "addi- tion" x y = xy and the "scalar multiplication" cox=xc. TOPSTO a) Show that the natural logarithm is a linear transformation from R+ to R. b) Show that the exponential function is a linear transformation from R to R+.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 32E

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