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LOGARITHM

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LOGARITHM. GRADE X. LOGARITHMS. STANDARD OF COMPETENCY. Be able to solve problems related to exponents, roots, and logarithms. BASE COMPETENCY. To use the rules of exponents, roots, and logarithms . LOGARITHMS. INDICATORS. Changing exponents to be logarithms and vice versa .

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LOGARITHM

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  1. LOGARITHM GRADE X

  2. LOGARITHMS STANDARD OF COMPETENCY Be able to solve problems related to exponents, roots, and logarithms BASE COMPETENCY • To use the rules of exponents, roots, and logarithms

  3. LOGARITHMS INDICATORS • Changing exponents to be logarithms and vice versa. • Using logarithm properties to solve a simple algebraic operation

  4. LOGARITHMS PROBLEM ? 32 = 9 2= ??? 3 Log 9 = 2

  5. LOGARITHMS Base, a>0, a≠1 Value a Log b = c Numerous, b>0

  6. LOGARITHMS Examples : 1. Express into logarithm form A. 23 = 8 C. 3x = 15 B. 25 = 32 D. 3(x+2) = 20 Answer : A. 23= 8  3 = 2Log 8 B. 25= 32  5 = 2Log 32 C. 3x= 15  x = 3Log 15 D. 3(x+2) = 20 x+2 = 3Log 20

  7. LOGARITHMS The LogarithmSFormulae m= aLog b am = b an = c bc = am. an = a m+n n = aLog c aLog(bc) = m + n = aLogb + aLog c aLog(bc) = aLog b + aLog c

  8. LOGARITHMS The Logarithm Formulae aLogbc = aLog b + aLog c aLog (b/c) = aLog b - aLog c aLogbn= n. aLog b a mLog b = (1/m) aLog b aLog a = 1, aLog 1 = 0 aLog b x bLog c = aLog c

  9. LOGARITHMS Examples : 2 Log 16 1. Find the values of the following A. B. C. Answer : A. B. 5 Log 125 Log 0,01 C. Log 0,01 = Log 10-2 = -2. Log 10 = -2.1 = -2 2 Log 16 = 2 Log 24 = 4. 2 Log 2 = 4 5 Log 125 = 5 Log 53 = 3 . 5 Log 5 = 3

  10. LOGARITHMS Examples : 2 Log 3 + 2 Log 8 – 2 Log 6 2. Simplify using logarithm properties ! A. B. Answer : A. B. 3Log 4 + 2.3 Log 2 – 2.3 Log 4 2 Log 3 + 2 Log 8 – 2 Log 6 = 2 Log (3x8) – 2 Log 6 = 2 Log (24/6) = 2 Log 4 = 2 3Log 4 + 2.3 Log 2 – 2.3 Log 4 = 3 Log 4 + 3 Log 22 – 3 Log 42 = 3 Log (4x4) – 3 Log 16 = 3 Log (16/16) = 3 Log 1 = 0

  11. LOGARITHMS EXERCISES • PAGE 55-56 • NO: 1 A, B, C, D, E • 2 A, B, D, E • 3 A, B, E • 4 A, B, C, D • 7 A, C • 8 • 9 A, B, C, D • 11 A, B

  12. LOGARITHMS THANK YOU

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