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+.

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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.
a) Show that the natural logarithm is a linear
transformation from R+ to R.
b) Show that the exponential function is a linear d
transformation from R to R+.
Transcribed Image Text: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. a) Show that the natural logarithm is a linear transformation from R+ to R. b) Show that the exponential function is a linear d transformation from R to R+.
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To answer the question we use the properties of natural logarithm and exponential functions and use the given definition of addition and scalar multiplication as follows.

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