Ex 3.4-9th class math-Logarithms-Q 4 part v and vi-FBISE
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Transcript
00:00In this video I am going to cover the part 5 and 6 of question 1 of exercise 3.4 which
00:22is related to the logarithm.
00:24So let's dive into the solution of the exercise 3.4 of question 1, 4, 5 and 6.
00:34Here is the question number 1 and this is part 5, 1.23 into 0.6975 divided by 0.0075
00:46into 1278, 1278, allow me to...
01:00Now solution, let y is equal to 1.23 into 0.6975 divided by 0.0075 into 1278, please
01:15you will put second parenthesis around this one as I have did previously with the question.
01:23Applying log on both sides, log y is equal to log 1.23 into 0.06975, 0.075 into 1478.
01:37So if you look at this equation, we have come to know that there is a two part numerator
01:46and denominator.
01:47In numerator there is a product of two terms, also in denominator there is a product of
01:53two terms.
01:55It means we are going to apply the two laws of logarithm, product laws of logarithm and
02:02quotient laws of logarithm.
02:05By applying product and quotient laws of logarithm we will get log y is equal to log 1.3 plus
02:11as product turns into plus positive log 0.6975 minus log 0.0075 minus log 1278.
02:22In case of quotient law, the elements are numbers that are variable in the positional
02:30denominator it turns into negative sign as there are two elements in the product form
02:35so first they turn into positive but after that when we are going to apply the quotient
02:41law the negative sign turns both positive signs into negative signs.
02:46So this 1.23 is equal to 0 as we go with the rule that, inspection rule that there
02:57is a one digit before decimal so 1 minus 1 is equal to 0 and for the second term of the
03:03numerator 0.6975 is equal to minus 1, there is no digit before that so 0 minus 1 is equal
03:10to minus 1 and 0.0075 if we will go from point on right hand side 1, 2, 2, 0 and we
03:22are going to put decimal after 3, 7 so how many digits we count 3 digits we count so
03:29minus 3, 1, 2, 7, 8 so we will move from right to left 8, 7, 2, 1.278 is equal to 3.
03:41Mentesia, remember that in case of Mentesia we are going to get significantly 4 digits
03:49round off after rounding off so 1, 2, 3 is equal to 0.899 when we will move to the log
03:59table and look this values 12 against 3 we will get this one now 6, 9, 7, 5 is equal
04:06to 69 under column 7, 3 and then 5 we will get 8, 4, 3, 2 plus 3, 8, 4, 3, 5, 7, 5, 7,
04:185 under 0, 8, 7, 5, 1, 1, 2, 7, 8 again 12 under column 7 and again under column 8 is
04:24equal to 1, 0, 3, 8 plus 27 is equal to 1, 0, 6, 5 thus by putting these values we will
04:32get log y is equal to 0.0899 plus as Mentesia is minus 1 so we will put bar on the 1, 8,
04:434, 3, 5 minus bar 3, 0.8751 and minus 3.1035 because it is positive 3 not negative 3 log
04:56y let me correct this log y is equal to 0.8991 minus 1 plus 0.8435 plus 3 minus 0.875 as
05:10this minus multiply by this minus it turn into positive and this is a positive it turns
05:15into negative minus 3.1065 ok log y by adding and subtracting all this we will get minus
05:411 minus 0.0482 by adding and subtracting 1 we will get log y is equal to 1 minus 1
05:49minus 1 is equal to minus 0.0482 this minus 1 minus 2 is equal to minus 2 plus by subtracting
06:00this from this one we will get 0.9815 is equal to 2 bar 0.9518 taking antilog of both sides
06:08antilog is equal to log y antilog 2 bar 0.9518 so now we are going to check this value into
06:16the antilog table so 0.95 under column 1 and 8 so 0.8933 plus 0.73 is equal to 0.8950 as
06:26the statistics minus bar 2 or minus 2 therefore to run this after that we will go into pole
06:380 and then we will place point the 0.0895 is our required answer now the last part of
06:45the question number 1 of exercise 3.4 of logarithm chapter 6 is here cube root 0.7214 into 0.7214
06:560.7214
07:000.7214
07:07let me correct this one this is 20.37 by mistake I have written this one point 20.37 and so we
07:23will correct this number on every step that will come to us that was equal to cube 0.7214
07:32into 20.37 divided by 60.8 0.7214 into 20.37 divided by 60.8 raised to power 1 by 3 then
07:46taking log of both sides log y is equal to log 0.7214 into 0 20.37 divided by 60.8 raised to
07:56power 1 by 3 apply indices rule here log y is equal to the power becomes a coefficient
08:03or multiplicative factor of this function or expression 1 by 3 into log 0.7214 into
08:1320.37 divided by 60.8 now applying product and quotient rules 1 by 3 log 0.7214 plus log 20.37
08:24minus log 60.8 statistics for the first number 0.7214 is equal to 1 bar for this 20.37 there
08:32are 2 digits 2 minus 1 1 60.8 again there are 2 digits 2 minus 1 is equal to 1 in mantissa
08:390.7214 in log tables you will see 72 value under 1 and 4 85 79 plus 285 89 20 under 3 and 7 307
08:55plus 1 5 3 0 9 0 and 6 0 8 is equal to 7 8 3 9 thus log y is equal to 1 by 3 bar 1 minus
09:08bar 1 point 8 5 8 9 plus 1 point 3 0 9 0 minus 1 point 7 8 9 3 minus 1 plus 0 point 8 5 8 1 plus
09:171 plus 0 point 3 0 9 0 minus 1 point 0 7 8 3 9 method 1 log y 1 by 3 minus 1 as this one is
09:31cancelled by this one so we will going to add this 1 point 8 5 8 1 and point 3 0 9 1 and then
09:43we will subtract this value from this one by adding a subtracting 2 we get log y is equal
09:50to 1 by 3 minus 1 plus 0 point 0 point 3 8 3 2 plus 2 minus 2 log y is equal to 1 by 3 minus 3
10:00plus this minus 2 is added this minus 1 minus 3 plus to add with this one so we will get minus
10:151 plus 20.7 9 9 4 something is wrong here 0.7 9 4 4
10:30by dividing and both element of both element of the expression inside the parentheses we
10:46got minus 1 plus 0.7 9 4 4 1 bar 0.7 9 4 4 taking antilog of both sides log y 0.6 2 2 9 answer this
10:56antilog will cancel by this and you look this value 0.7 9 enter column 4 and 4 under antilog
11:04table you will get this value and you will place 1 bar so you will go 6 then before 6 you will
11:14place point and then 0 method 2 1 by 3 1 point 1 6 7 1 minus 1 point 7 8 3 9 let me go back to
11:24this one this step so by adding these we will get this one 1 by 3 1 point 1 6 7 1 minus 1 point 7
11:378 3 9 by adding a subtracting 3 we will get 1 by 3 minus 3 plus 3 plus 1 point 1 6 7 1 minus 1 point
11:477 8 3 9 and minus 3 plus this 3 added by this one 4.1 6 7 1 minus 1 point 7 8 9 3 now I am going
11:59to be solve this expression by subtracting this from positive 4.1 6 7 1 will get minus 3 plus 2
12:10point 3 8 3 2 and now divided both the element of this inside square brackets by 3 we will get
12:23minus 1 plus 0.7 9 4 4 is equal to 1 bar 0.7 9 4 4 taking antilog of both sides antilog 1 bar 1
12:36point 7 9 4 4 is equal to 6 2 2 3 plus 6 6 2 2 9 9 as that is 6 is 1 bar so we will place 0 immediately
12:47before 6 point 6 2 2 9 this is our required answer so I hope you will find this video useful if you
12:57have any question or query about any step of of related to these two questions please ask me in
13:05the comment section inshallah I will reply you thanks for watching assalamu alaikum