Practice with Logarithm

Try to answer the question of logarithm with your own. If not sure with your answers, you may check answer at the bottom..

1.	Which of the following statements is not correct?
	A. log10 10 = 1 B. log (2 + 3) = log (2 x 3) C. log10 1 = 0 D. log (1 + 2 + 3) = log 1 + log 2 + log 3

---

2.	If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:
	A. 2.870 B. 2.967 C. 3.876 D. 3.912

---

3.	log 8 is equal to: log 8
	A. 1 8 B. 1 4 C. 1 2 D. 1 8

---

4.	If log 27 = 1.431, then the value of log 9 is:
	A. 0.934 B. 0.945 C. 0.954 D. 0.958

---

5.	If log a + log b = log (a + b), then: b a
	A. a + b = 1 B. a - b = 1 C. a = b D. a2 - b2 = 1

Answer the above question: Answer #1: Option B Explanation: (a) Since loga a = 1, so log10 10 = 1. (b) log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3       log (2 + 3)  log (2 x 3) (c) Since loga 1 = 0, so log10 1 = 0. (d) log (1 + 2 + 3) = log 6 = log (1 x 2 x 3) = log 1 + log 2 + log 3. So, (b) is incorrect. Answer #2: Option C Explanation: log5 512 = log 512 log 5 = log 29 log (10/2) = 9 log 2 log 10 - log 2 = (9 x 0.3010) 1 - 0.3010 = 2.709 0.699 = 2709 699 = 3.876 Answer #3: Option C Explanation: log 8 = log (8)1/2 = log 8 = 1 . log 8 log 8 log 8 2 Answer #4: Option C Explanation: log 27 = 1.431  log (33 ) = 1.431  3 log 3 = 1.431  log 3 = 0.477  log 9 = log(32 ) = 2 log 3 = (2 x 0.477) = 0.954. Answer #5: Option A Explanation: log a + log b = log (a + b) b a  log (a + b) = log a x b = log 1. b a So, a + b = 1. That's all from me, you may try as many as you can to improve your knowledge.. If you still don't understand, refer to the example that I have been given :) Wish you have Luck!