By converting to exponential form, find the values of : (i) log 2 16 (ii) log 5 125 (iii) log 4 8 (iv) log 9 27 (v) log 10 (0.01) (vi) log 7 (vii) log 0.5 256 (viii) log 2 0.25

(i) log 2 16 = x ⇒ 2 x = 16 ⇒ 2 x = 2 4 ∴ x = 4. Hence, log 2 16 = 4. (ii) log 5 125 = x ⇒ 5 x = 125 ⇒ 5 x = 5 3 ∴ x = 3. Hence, log 5 125 = 3. (iii) log 4 8 = x ⇒ 4 x = 8 ⇒ (2 2 ) x = 2 3 ⇒ 2 2x = 2 3 ⇒ 2x = 3 ⇒ x = Hence, log 4 8 = . (iv) log 9 27 = x ⇒ 9 x = 27 ⇒ (3 2 ) x = 3 3 ⇒ 3 2x = 3 3 ⇒ 2x = 3 ⇒ x = Hence, log 9 27 = . (v) log 10 (0.01) = x ⇒ 10 x = 0.01 ⇒ 10 x = 10 -2 ∴ x = -2. Hence, log 10 (0.01) = -2. (vi) log 7 = x ⇒ 7 x = ⇒ 7 x = 7 -1 ∴ x = -1. Hence, log 7 = -1. (vii) log 0.5 256 = x ⇒ (0.5) x = 256 ⇒ = (2) 8 ⇒ = (2) 8 ⇒ (2) -x = (2) 8 ∴ -x = 8 ⇒ x = -8. Hence, log 0.5 256 = -8. (viii) log 2 0.25 = x ⇒ 2 x = 0.25 ⇒ 2 x = ⇒ 2 x = ⇒ 2 x = 2 -2 ⇒ x = -2. Hence, log 2 0.25 = -2.

Mathematics

By converting to exponential form, find the values of : (i) log216 (ii) log5125 (iii) log48 (iv) log927 (v) log10 (0.01) (vi) log7 (vii) log0.5 256 (viii) log2 0.25

Logarithms

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Mathematics

By converting to exponential form, find the values of : (i) log<sub>2</sub>16 (ii) log<sub>5</sub>125 (iii) log<sub>4</sub>8 (iv) log<sub>9</sub>27 (v) log<sub>10</sub> (0.01) (vi) log<sub>7</sub> (vii) log<sub>0.5</sub> 256 (viii) log<sub>2</sub> 0.25

Logarithms

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Mathematics

By converting to exponential form, find the values of : (i) log<sub>2</sub>16 (ii) log<sub>5</sub>125 (iii) log<sub>4</sub>8 (iv) log<sub>9</sub>27 (v) log<sub>10</sub> (0.01) (vi) log<sub>7</sub> (vii) log<sub>0.5</sub> 256 (viii) log<sub>2</sub> 0.25

Logarithms

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