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قوانين اللوغاريتمات

(a) log_b 14 = log_b (2 x 7)

    = log_b 2 + log_b 7

    ≈ 0.43 + 1.21 ≈ 1.64

(b) log_b  = log_b 2 - log_b 7

                  ≈ 0.43 - 1.21 ≈ -0.78

(c) log_b 32 = log_b 2⁵ = 5 log_b 2

                  ≈ 5 x 0.43 ≈ 2.15

(d) log_b  = log_b 1 - log_b 49

                   = 0 - log_b 7²

                   ≈ 0 – 2 log_b 7

                   ≈ 0 - 2 x 1.21 ≈ -2.42

(a) log₂ a² b⁹ = log₂ a² + log₂ b⁹

                       = 2 log₂ a + 9 log₂ b

(b) log₅  = log₅ (x + 1)³ – log₅ 8

                            = 3 log₅ (x + 1) – log₅ 8

(c) log₃  = log₃ x⁷ y³ – log₃ z⁵

                        = log₃ x⁷ + log₃ y³ – log₃ z⁵

                        = 7 log₃ x + 3 log₃ y – 5 log₃ z

(d) log_b  = log_b ()

                            =  log_b 

                            =  (log_b x⁷ b² - log_b y⁵)

                            =  (log_b x⁷ + log_b b² – log_b y⁵)

                            =   (7 log_b x + 2 log_b b – 5 log_b y

                            =   log_b x + log_b b – log_b y

                            =  log_b x + - log_b y

(a) log₅ a + 3 log₅ b = log₅ a + log₅ b³

                                 = log₅ ab³

(b) 5 log_b x +  log_b y – 9 log_b z  

                       = log_b x⁵ + log_b  - log_b z⁹

                       = log_b x⁵ - log_b  z⁹

                       = log_b 

                       = log_b 

M(t) = 92 – 28 log₁₀ (t + 1)

M(29) = 92 – 28 log₁₀ (29 + 1)

            = 92 – 28 log₁₀ 30

            = 92 – 28 log₁₀ (10 x 3)

            = 92 – 28 (log₁₀ 10 + log₁₀ 3)

            ≈ 92 – 28 (1 + 0.4771)

            ≈ 92 – 28 (1.4771)

            ≈ 92 – 41.3588

            ≈ 51

النسبة المئوية للموضوعات التي يتذكرها هذا الطالب بعد 29 شهراً هي 51% تقريباً.