Unit#3 Logarithms Exercise 3.4 And Review Exercise3 3v3kg

Unit 3 Logarithms Exercise 3.4 Question # 1 Use log tables to find the value of the following: (i)

0.8176 x 13.64

Solution 0.8176 x 13.64 Let x = 0.8176 x 13.64 Taking log of both sides log x =log( 0.8176 x 13.64) log x = log 0.8176 + log 13.64 log x = .9125 + 1.1348 log x = -1 + 0.9125 + 1 + 0.1348 log x = 0.9125 + 0.1348 log x = 1.0437 x = Antilog (1.0437) Ch = 1 Mantissa = .0437 X = 11.06 (ii)

(789.5)1/8

Solution Mudassar Nazar Notes Published by Asghar Ali

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(789.5)1/8 Let x = (789.5)1/8 Taking log of both sides log x = log (789.5)1/8 log x = log 789.5 log x = ( 2.8974) log x = 0.3622 x = Antilog 0.3622 Ch = 0 Mantissa = .3622 x = 2.303

(iii) Solution

Let x = Taking log of both sides log x = log(

)

log x = log 0.678 + log 9.01 – log 0.0234 log x = .8312 + 0.9547 - .3692 log x = [-1 + 2 ] + [ 0.8312 + 0.9547 – 0.3692] log x = 1 + 1.4167 Mudassar Nazar Notes Published by Asghar Ali

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log x = 2.4167 x = Antilog 2.4167 Ch = 2 Mantissa = .4167 x = 261 (iv)

x

Solution

x Let x = (2.709)1/5 x (1.239)1/7 Taking log of both sides log x = log [(2.709)1/5 x (1.239)1/7] log x = log(2.709)1/5 + log (1.239)1/7 log x = log 2.709 + log 1.239 log x = (0.4328) + (0.0931) log x = 0.0866 + 0.0133 log x = 0.0999 x = Antilog 0.0999 Ch = 0 Mantissa = .0999 x = 1.259 (v) Solution

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Let x= Taking log of both sides log x = log log x = log 1.23 + log 0.6975 –[ log 0.0075 + log 1278] log x = 0.0899 + .8435 –[ .8751 + 3.1065] log x = 0.0899 + .8435 - .8751 – 3.1.65 log x = 0.0899 – 1 + 0.8435 + 3 - 0.8751 – 3 - 0.1065 log x = (-1 + 3 + 3) + ( 0.0899 + 0.8435 – 0.8751 – 0.1065) log x = -1 – 0.0482 log x = -1.0482 log x = + (2 -1.0482) log x = + 0.9518 log x = .9518 Ch = 8933 17 8^950 = 0.0895 + Mantissa = .9518 x = 0.0895

(vi) Solution

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Let x= ] 1/3

x=[ Taking log of both sides

] 1/3

log x = log [ log x = log

log x = [ log 0.7214 + log 20.37 – log 60.8] log x = [ .8581 + 1.3090 – 1. 7839] log x = [-1 + 0.8581 + 1 + 0.3090 – 1 . 7839] log x = [ 0.8581 + 0.3090 – 1 . 7839] log x = [-0.6168] log x = -0.2056 log x = + (1 – 0.2056) log x = + 0.7944 log x = .7944 x = Antilog

.7944

Ch =

6223 6 6^229 = 0.6229 +

Mantissa = .7944 x = 0.6229 (vii) Solution

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Let x = Taking log of both sides log x = log log x = log 83 + log (92)1/3 – log 127 – log (246)1/5 log x = log 83 + log 92 – log 127 - log 246 log x = 1.9191 +

(1.9638) – 2.1038 - (2.3909)

log x = 1.9191 +0.6546 – 2.1038 - 0.4782 log x = -0.0083 log x = + ( 1 – 0.0083) log x = + 0.9917 log x = .9917 Ch =

9795 16 9^811 = 0.9811 +

Mantissa = .9917 x = 0.9811 (viii) Solution

Let x= Taking log of both sides

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log x = log [

]

log x = log (438)3 + log (0.056)1/2 – log (388)4 log x = 3 log 438 + log 0.056 – 4 log 388 log x = 3(2.6415) + ( .7482) – 4(2.5888) log x = 7.9245 + .3741 – 10.3552 log x = 7.9245 – 1 + 0.3741 – 10.3552 log x = 8.2986 – 11.3552 log x = - 3.0566 log x = + ( 4 – 3.0556) log x = + 0.9434 log x = .9434 x = Antilog ( .9434)

8770 8 8^778 = 0.0008778 +

Ch = Mantissa = .9434 x = 0.0008778

Example # 2

Solution

Let x = Mudassar Nazar Notes Published by Asghar Ali

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Taking log of both sides log x = log log x = log log x =

[ log 0.07921 + 2 log 18.99 – 4 log 5.79 – log 0.9474

log x =

[ .8988 + 2(1.2786) – 4 (0.7627) - .9765]

log x =

[-2 + 0.8988 + 2.5572 –3.0508 + 1 – 0.9765]

log x =

[-2 + 0.8988 + 2 + 0.5572 –3 - 0.0508 + 1 – 0.9765]

log x =

[(-2+2 -3 + 1) +( 0.8988 + 0.5572 –0.0508 – 0.9765]

log x =

[ + 0.4287]

log x =

[ +1 + 0.4287]

log x =

[ +1.4287]

log x = + 0.4762 log x = .4762 x = Antilog .4762 Ch = Mantissa = .4762

2992 1 2^993 = 0.2993 +

x = 0.2993

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Review Exercise 3 Question # 6 Simplify the following: (i) Solution

Let x = (25.47)1/3 Taking log of both sides log x = log (25.47)1/3 log x = log 25.47 log x = ( 1.4060) log x = 0.4687 x = Antilog 0.4687 Ch = 0 Mantissa = .4687 x = 2.942

(ii) Solution

Let x= Taking log of both sides Mudassar Nazar Notes Published by Asghar Ali

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logx = log logx = log(324.2) logx = ( 2.5343) logx = 0.5069 x = antilog (0.5069) Ch = 0 Mantissa = .5069 x = 3.213

(iii) Solution

Let x= Taking log of both sides log x = log log x = log(8.97)3 + log (3.95)2 – log (15.37)1/3 log x = 3log 8.97 + 2 log 3.95 - log 15.37 log x = 3(0.9528) + 2( 0.5966) - ( 1.1867) log x = 2.8584 + 1.1932 – 0.3956 log x = 3.6560 x = Antilog 3.6560 Mudassar Nazar Notes Published by Asghar Ali

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Ch = 3 Mantissa = .6560 x = 4529

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