Logarithm Worksheet Express the equation in exponential form

Logarithm Worksheet Express the equation in exponential form. 2. loge 2 1/3 1, logs 25 2 Express the equation in logarithmic form. 4.81: 1/8 3.53 125 Evaluate the expression. 5. (a) loge, 36 (b) logg 81 (c) log77 6. (a) loga (1/27) (b) logio N10 (c) logs 0.2 7. (a) 2 92 37 (b) 3\'09, 8 (c) ele (c) 10log 87 (b) 10log5 In T 8. (a) e Use the definition of the logarithmic function to find x (b) logio 0.1 x 9. (a) log15 x 4 10. (a) log4 2 x (b) log4 x 2 (b) log 25 2 11. (a) logx1000 Use a calculator to evaluate the expression, correct to four decimal places (b) In 25.3 (c) (1 V3 12. (a) In 5 13. (a) In 27 (b) In 7.39 (c) in 54.6 Find the domain of the function. 15. f(x) log5(8- 2x) 14. f(x) logio(x 3)

Solution

1. log₅ 25 = 2, then 25 = 5^{2 ;} 2. log₈ 2 = 1/3, then 2 = 8^1/3

3. 5³ = 125, then 3 = log₅ 125 ; 4. 8^-1 = 1/8, then -1= log₈ (1/8)

5. (a) log₆ 36=log₆ 6² =2 log₆ 6 =2;(b) log₉ 81 = log₉ 9² =2log ₉ 9 =2 ;(c) log₇ 7¹⁰= 10log₇ 7 = 10

6. (a) log₃ (1/27)= log₃( 3^-3) = -3log₃ 3 = -3; (b) log₁₀10 = log₁₀(10)^1/2 = 1/2 log₁₀ 10 = 1/2; (c)  log₅ 0.2=log₅ (1/5) = log₅ 5^-1=-1log₅ 5 = -1  

7. 2^log₂37 = 37 ( if 2^log₂37 = a, then on taking log to the base 2, we have ( log₂ 37)(log₂ 2) = log₂ a or, log₂ 37 = log₂ a so that a = 37) ; (b) 3^{log₃ 8} = 8 ; (c) e (^ln5) = 5

8. (a) e^(ln ) = ; (b) 10^{log 5} = 5 ( if the base of log is not mentioned, it is assumed to be10) ; (c) 10^{log 87} = 87

9.(a) log₅ x = 4, then x = 5⁴ = 625 ; (b) log₁₀ (0.1) = x or, x = log₁₀(10^-1) = -1 log₁₀ 10 = -1

10(a) log₄ 2 = x or, x = log₄ (4)^1/2 = (1/2) log₄ 4 = 1/2 ; (b) log₄ x = 2, then x = 4² = 16.

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