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Mastering the Laws of Logarithms for Real Numbers B

Explore laws of logarithms, solve equations, simplify expressions, and express in terms of logs with helpful examples. Enhance your mathematical skills!

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Mastering the Laws of Logarithms for Real Numbers B

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  1. Laws of Logarithms 5.6

  2. Laws of Logarithms • If M and N are positive real numbers and b is a positive number such that b  1, then • 1. logbMN = logbM + logbN • 2. logb = logbM - logbN • 3. logbM = logbN if and only if M = N • 4. logbMk = klogbM, for any real number k.

  3. Laws of Logarithms • 5. • 6. • 7. • 8. *ln has the same laws.

  4. Ex. Write each expression in terms of Log M and log N. • A) log • B) • C) log M2

  5. Ex. Write each expression as a rational number or as a single logarithm. • A) ln 2 + ln 6 – ln 9 • B) log6 9 + log 6 5 • C) log 3 – log 6 – log 5 • D) (2logb M – logb N – log b P)

  6. Ex. Simplify each expression with out a calculator. • A) lne2 B) ln • C) ln e3x + 5 D) 102 log 6 • E) 103 + log 4 F) e1 + 2 lnx

  7. Ex. Solve the given equation. • A) log 2 (x + 2) + log 2 5 = 4 • B) log 4 (2x + 1) – log 4 (x – 2) = 1

  8. Ex. Express y in terms of x • Ex. 6 Given log 43 = x & log 47 =y, write the following in terms of x and y: • log 463

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