Assume thatL(a) = lim x0 ax 1 x exists for all a > 0.Assume also that limx0 ax = 1. (a)
Chapter 2, Problem 42(choose chapter or problem)
Assume thatL(a) = lim x0 ax 1 x exists for all a > 0.Assume also that limx0 ax = 1. (a) Prove that L(ab) = L(a) + L(b) for a, b > 0. Hint: (ab)x 1 = ax bx ax + ax 1 = ax (bx 1) + (ax 1). This shows that L(a) behaves like a logarithm, in the sense that ln(ab) = ln a + ln b. We will see that L(a) = ln a in Section 3.9. (b) Verify numerically that L(12) = L(3) + L(4).
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