Explanation Given: The equation, ( ln x ) 2 − ln x 5 = − 4 Formula used: The power property of logarithm is log a b = b log a . Calculation: The provided equation is, ( ln x ) 2 − ln x 5 = − 4 ( ln x ) 2 − ln x 5 + 4 = 0 Use power property of logarithm ( ln x ) 2 − 5 ln x + 4 = 0 Substitute ln x = u u 2 − 5

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ISBN: 9780078035616

Author: Julie Miller

Publisher: MCG

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Chapter 4.5, Problem 117PE

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To calculate: The solution set for the equation (lnx)2−lnx5=−4.

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Chapter 4.5, Problem 116PE

Chapter 4.5, Problem 118PE

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R denotes the field of real numbers, Q denotes the field of rationals, and Fp denotes the field of p elements given by integers modulo p. You may refer to general results from lectures. Question 1 For each non-negative integer m, let R[x]m denote the vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m. x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent (a) Let vi = x, V2 = list in R[x] 3. (b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4) is a basis of R[x] 3. [8] [6] (c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a linear map. [6] (d) Write down the matrix for the map ƒ defined in (c) with respect to the basis (2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3. [5]

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part b please

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The solution set for the equation ( ln x ) 2 − ln x 5 = − 4 .

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Chapter 4 Solutions