LOGARITHM GRADE X LOGARITHMS STANDARD OF COMPETENCY Be

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. - Using logarithm properties to solve a simple algebraic operation

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

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

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

LOGARITHMS The Logarithm. S Formulae m= a. Log b n = a. Log c am = b an = c bc = am. an a. Log = a m+n a (bc) = m + n = a. Log b + a. Log c Log (b c) = a. L og b + a Log c

LOGARITHMS The Logarithm Formulae a. Log bc = a. Log b + a. Log c a. Log (b/c) = a. Log b - a. Log c bn = n. a. Log b a m Log a = 1, a. Log b = (1/m) a. Log b 1=0 a. Log b x b. Log c = a. Log c

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

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

LOGARITHMS EXERCISES PAGE NO: 55 -56 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

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