To prove Proprieties P1, P2, P3, and P7 of Theorem 3 , let X = log a M and Y = log a N , and give reasons for the steps listed in Exercises 119 – 122. Proof of P1 of Theorem 3 M = a X and N = a Y , definition of logarithm So M N = a X ⋅ a Y = a X + y Product Rule for exponents Thus, log a ( M N ) = X + Y definition of logarithm = log a M + log a N . substitution
To prove Proprieties P1, P2, P3, and P7 of Theorem 3 , let X = log a M and Y = log a N , and give reasons for the steps listed in Exercises 119 – 122. Proof of P1 of Theorem 3 M = a X and N = a Y , definition of logarithm So M N = a X ⋅ a Y = a X + y Product Rule for exponents Thus, log a ( M N ) = X + Y definition of logarithm = log a M + log a N . substitution
Solution Summary: The author explains the reasons behind each step for the proof of the logarithmic property mathrmlog_a(MN)=
2. a) Express log, 3 in terms of a logarithm to base 3.
64. Find the largest integern such that log* n = 5. Determine
the number of decimal digits in this number.
Exercises 65–67 deal with values of iterated functions. Sup-
pose that f(n) is a function from the set of real numbers, or
positive real numbers, or some other set of real numbers, to
the set of real numbers such that f(n) is monotonically increas-
ing [that is, f(n) 0.
ighoman
Furthermore, let c be a positive real number. The iterated
function f* is the number of iterations of f required to reduce
its argument to c or less, sof*(n) is the smallest nonnegative
integer k such that fk (n) < c.
13
C
C
If log, 2,log,o (2* - 1) and log,o (2" + 3) are in A.P
then find the value of x.
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How to determine the difference between an algebraic and transcendental expression; Author: Study Force;https://www.youtube.com/watch?v=xRht10w7ZOE;License: Standard YouTube License, CC-BY