Categories
Mathematics

Laws of Logarithm

  1. a) let P = bx, then logbP = x

Q = by, then logbQ = y

PQ = bx X by = bx+y (laws of indices)

LogbPQ = x + y

:.             LogbPQ = logbP + LogbQ

  1. b) P÷Q = bx÷by = bx+y

LogbP/Q = x –y

:.             LogbP/Q = logbP – logbQ

  1. c) Pn= (bx)n = bxn

Logbpn = nbx

:.             LogPn = logbP

  1. d) b = b1

:.             Logbb = 1

  1. e) 1 = b0

Logb1 = 0

EXAMPLE – Solve each of the following:.

  1. a) Log327 + 2log39 – log354
  2. b) Log35 – log310.5
  3. c) Log28 +  log23
  4. d) given that log102 = 0.3010 log103 = 0.4771 and log105 = 0.699 find the log1064 + log1027

Solution

  1. a) Log327 + 2 log39 – log354

= log3 27 + log3 92 –log354

= log3 (27 X 92/54)

= log3 (271 X 81/54) = log3 (81/2)

= log3 34/log32

= 4log3 3 – log3 2

4 X (1) – log3 2 = 4 – log3 2

= 4 – log2

  1. b) log5 – log10.5

= log(13.5)- Log310.5 = log(135/105)

= log(27/21) = log27 – log21

= log3 – log(3 X 7)

= 3log3  – log3 -log37

= 2 – Log7

  1. c) Log28 + Log33

= log223+ log33

= 2log22 + log33

2+1=3

  1. d) log10 64 + log10 27

log10 26 + log1033

6 log10 2 + 3 log10 3

6 (0.3010) + 3(0.4771)

1.806 + 1.4314 = 3.2373.

EVALUATION ( USE THE DISCUSSION BOX AT THE BOTTOM TO SUBMIT YOUR ANSWER FOR DISCUSSION AND APPRAISAL)

  1. Change the following index form into logarithmic form.

(a)          63= 216 (b) 33 = 1/27        (c) 92 = 81

  1. Change the following logarithm form into index form.

(a)          Log88 = 1              (b) log ½¼ = 2

  1. Simplify the following
  2. a) Log55 + log52
  3. b) ½ log48 + log432 – log42
  4. c) Log381
  5. Given that log 2 = 0.3010, log3 0.477

Log105 = 0.699, find the log10 6.25 + log10

Join Discussion Forum and do your assignment: Find questions at the end of each lesson, Click here to discuss your answers in the forum

Ad: Get a FREE Bible: Find true peace. Click here to learn how you can get a FREE Bible.

For advert placement/partnership, write ask@stoplearn.com

Download our free Android Mobile application: Save your data when you use our free app. Click picture to download. No subscription. stoplearn

We are interested in promoting FREE learning. Tell your friends about Stoplearn.com. Click the share button below!