Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Functions - Logarithmic functions - Log Laws.
Test Yourself 2.

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Use the six laws of logarithms as outlined in the video to simplify/solve the following:

Log laws with numbers.	1. Simplify log2 48 - log2 3. Answer.4.	2. Evaluate correct to 3 significant figures: log4 32 - log4 5. Answer.1.34.
	3. Find the value of log5 200 - 3log5 2. Answer.2.	4.
	5. Simplify . Answer.-2.	6. Find the value of J (to 2 decimal places) if log3 5 + log2 9 = J Answer.4.63.
	7. If , find the values of p and q. Answer.p = 5 and q = -3.	8. Show .
Log laws with pronumerals.	9. Simplify log3 81x - log3 9x Answer.2.	10.
	11. Simplify . Answer.2.	12. If log x + log y = log (x+y), prove
	13.
	15.	16.
	17. If where a > 0 and N > 0, show y = loga N.	18.
	19. Change the subject of the following equation to y in a form not involving any logarithms: 2log2 x + log2 y = 3. Answer.y = 8/x2	20.
	21.	22.
	23.	24.
	25.	26.
	27. Simplify . Answer.value = 1.
	28.
Substitution	29. If log pq = 1.544 and log qr = 1.113, find the value of . Answer.value = 0.431.	30. If log 2 = a and log 3 = b and log 5 = c, express each of the following in terms of a, b and c: (i) log 45 (ii) (iii) . (iv) . Answer.(i) 2b + c. (ii) a + b - 2c (iii) 1/2(2a + 2c - 3b) (iv) 1/4(a - 2c).
	31. It is given that loga b = 2.75 and that loga c = 0.25. Hence find the value of (i) (ii) loga (bc)2. Answer.(i) 2.5. (ii) 6.	32. Given x = log10 2 and y = log10 3 find in terms of x and y: (i) log10 15 (ii) log10 0.27.
Equations	33. If y = loga (7x - b)+ 3 , change the subject of the equation to x.	34. Solve 2 ln x = ln (5 + 4x). Answer.x = 1 but x ≠ -5.
	35. Solve log10 x2 + 3 = log10 x5 Answer.x = 10.	36. Solve 2log5 3 = log5 x - log5 6. Answer.x = 54.
	37. Solve 2log2 x - log2 (x+4) = 1 Answer.x = 4 NOT -2.	38. Solve loge x - loge (x-4) = loge 2 Answer.x = 8.
	39. Solve (log10 x3)(log10 x) + log10 x4 - 7 = 0 Answer.x = 10-7/3 or x = 10.	40. Solve log3 (2x - 7) = 2. Answer.x = 8.
	41. Solve log5 (4 - x) = 1 + 2 log5 x Answer.x = 4/5.	42. Solve 3log72 = log7x - log75. Answer.x = 40.