Logarithms-Ex 3.4-Class 9th Math-FBISE-Application of Laws of Logarithms

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Logarithms-Ex 3.4-Class 9th Math-FBISE-Application of Laws of Logarithms  Exercise 3.4 Q No 1 Use the log tables to find the value of i.     0.8176 X 13.64 ii.     〖(789.5)〗^(1/8) iii.      (0.678x9.01)/(0.0234) iv. √(5&2.709) X √(7&1.239)  #digilearnerspoint , #Logarithms , Ex 3.4, Class 9th Math, #FBISE,  Application of Laws of Logarithms, Laws of Logarithms, indices rule of logarithms, learn logarithms in easy way, learn logarithms online, rules of logarithms with examples, properties of logarithms, common log, natural log, logarithms class 9 ex 3.2, logarithms basics, characteristics and mantissa,  common logarithm, natural logarithm, John Napier, decadic logarithm, log with base 10, log with base e,  natural log in mathematics, Laws of Logarithms class 9th, derive laws of logarithms, logarithmic equations, change of base,

Transcript

00:00In the name of Allah, the most Gracious, the most Merciful.

00:13Peace be upon you, dear students and viewers.

00:15In today's video, we are going to do the exercise 3.4 of our logarithm chapter.

00:23Before starting the exercise, we are going to do an important example.

00:29After that, we will see the complete exercise 3.4.

00:32Applications of the Laws of Logarithm in Numerical Calculation

00:38This is an example.

00:39a is equal to a base 0 e raised to the power minus kd.

00:44If k is equal to 2, then what should be the value of 1?

00:49You can say that this is the level of the equation 1.

00:54a is equal to a base 0 divided by 2.

01:00Put the value of k and a in 1.

01:06a base 0 divided by 2 is equal to a0 e raised to the power minus 2d.

01:14Because k value is 2.

01:17Now, 1 divided by 2 is equal to e raised to the power minus 2d.

01:28This a0 is considered to be a0 available on the left hand side of the equation.

01:35Now, taking common log of both sides.

01:37Common log means the log which has base 10, this one.

01:41Log 10 1 by 2 is equal to log base 10 2 e raised to the power minus 2d.

01:46Applying quotient rule and power rule.

01:50Log base 10 to 1 minus log base 10 to 2 is equal to minus 2d.

01:58This power becomes coefficient or multiplier of the log base 10 to e.

02:050 minus 0.0301.

02:09Log base 10 to 1 is 0.

02:14And log base 10 to 2 is equal to 0.301 is equal to minus 2d.

02:20Log base 10 to e is equal to 2.718.

02:290.301 is equal to minus 2d into.

02:35Here, I have put the value of e which is equal to 2.718.

02:38Now, I am going to check these values into the log table to get this value 0.4343.

02:48So, dividing both sides by 0.434 into 2.

02:59We get d is equal to 0.3466.

03:03This minus is cancelled out by this minus.

03:10Let me correct it here.

03:12So, this is our required answer.

03:14Now, we are going to start exercise 3.4.

03:17The first question is here.

03:19Use the log table to find the value of 0.8176 into this x means multiplication here 13.64 solution.

03:31Let we give a name to this numerical expression which is y is equal to 0.8176 into 13.64.

03:44Now, taking log on both sides.

03:46Log y is equal to log 0.8176 into 13.64 as the numerical expression is in the form of product.

03:56So, we are going to apply the product laws of logarithm here.

04:00Log y is equal to log 0.8176 plus log 13.64.

04:05You have noticed that in log product the multiplication sign turns into the positive sign.

04:12Now, we are going to find the statistics of the two given numbers.

04:180.8176 is minus 1 because we start from point and there is no number is before point.

04:29There is 0.

04:30So, we are going to put minus 1 here.

04:32And how many digits are there before point 3, 1 or 2.

04:38So, we will subtract 1 from 2.

04:40We will get statistics of 1 for this 13.64.

04:46Mantissa, consider only 4 significant digits.

04:510.8176, 13.64, this one, 9.122 plus 3 and 13.35 plus 13.

05:06And by adding this one, we will get this.

05:10Log y is equal to, this is the log value of these two given numbers.

05:17So, minus 1.9125 plus 1.1348.

05:24When you will visit the log table, not antilog table, log table you will see this.

05:31Number 81 against the same horizontal line against the 7.

05:37And then again in the second, third part of the log table under 6.

05:44So, this is the way we have got the log values of these two numbers.

05:50And now we are going to put minus 1.

05:53Minus 1, it means statistics is minus 1.

05:58So, we read it as bar 1.9125 plus 1.1348.

06:04So, I am going to be split into this one, minus 1 plus 0.9125 plus 1 plus 0.1348.

06:13And we will get log y is equal to 1.0473.

06:22Taking antilog of both sides, look at this antilog is cancelled out by this log and only y is remaining.

06:30And now we are going to move to the antilog tables to find the values of 0.0473.

06:37This is our mantissa.

06:39Always remember that when you are going to use antilog table, you only focus on the mantissa.

06:45Because this first digit before point stands for statistics here.

06:52So, currently ignore it.

06:56And now look only decimal portion into the antilog tables that 0.0473.

07:011114 plus 1 is equal to 1115.

07:07As statistics is 1, so we are going to add 1 into this one.

07:12Therefore, add 1 to get position of decimal which is 2.

07:17So, we are move from left to right 1, 2.

07:22After that we will place the point here.

07:26And this is our required answer.

07:28Now we are going to move to the second part of the first question which is 789.5 raised to power 1 by 8.

07:36This is our exponent is involved here.

07:39Let y is equal to 789.5 raised to power 1 by 8.

07:43Taking log of both sides.

07:45Let log y is equal to log 789.5 raised to power 1 by 8.

07:55As this power becomes coefficient of the log number.

07:59So, under the rule of...

08:02And this is the exponent rule of logarithms.

08:051 by 8 into log 789.5.

08:10Statistics is here.

08:11Look at this how many digits are there.

08:13Before point, there are 3 digits.

08:16So, we are going to subtract 1 to get the statistics of this number.

08:20So, we have statistics 3 minus 1 is equal to 2.

08:23And this has been determined by the inspection method.

08:27So, mantissa is equal to 789.5.

08:31We consider 4 significant digits.

08:33Log 78 under column 9 and 5.

08:361 by 8, 8971 plus 3.

08:412.8971 is equal to 0.3621 also divided by 8.

08:46Now, we are going to check this 0.3621 into the table.

08:53So, we will get this 2302 plus log y is equal to 0.3621.

08:59Here, statistics is 1.

09:02Taking antilog of both sides.

09:04Antilog y is equal to antilog 0.3621.

09:092301 plus 1 and 2302.

09:12So, answer is 2.302.

09:20Now, we are going to move to the part 3 of the question number 1.

09:28Here is the part 3.

09:300.678 into 9.01 divided by 0.0234.

09:37Now, look at this.

09:39We have product and quotient in this part.

09:43So, we are dealing with the product and quotient rules of logarithm in this question.

09:50So, let y is equal to 0.678 into 9.01 divided by 0.0234.

09:57Taking log of both sides.

09:59Log y is equal to log.

10:01By applying product and quotient rule of logarithm, we will get log 0.0678.

10:07Plus this multiplication sign turns into positive.

10:11Log into 9.01 divided by log 0.0234.

10:17If you apply the quotient rule here, you can write it like this.

10:22Minus log 0.0234 as well.

10:26Statistics is 1 bar 1.

10:30And for the 9.01, the statistics is 0.

10:33Because for decimal, there is only 1 digit.

10:361 minus 1 is equal to 0.

10:38And for 0.0234, the statistics is bar 2.

10:45Means how many zeros are offered after decimal.

10:52Only one zero and two digits.

10:54So, 1 and 2.

10:57So, statistics is bar 2.

10:59Now, we are going to deal with the mantissa.

11:020.0678 is 8312.

11:05You will get this value from the log tables.

11:08You will see 67 in the same horizontal line under the column 8.

11:13So, you will get this 8312 value.

11:16And log value is 1 bar minus 8312.

11:20For 9.01 is 9547.

11:24Here you look 90.

11:27Value of 90 and guess.

11:31Column 1, under the same horizontal line, you will get 9547.

11:35And log value is 0.9547.

11:39Because statistics is 0.

11:41For 0.0234 is 3692.

11:45And the log value is 2 bar 2.3692.

11:49Thus, log y is equal to bar 1 minus 0.8312 plus 0.9547 minus.

11:58Because it is available in the denominator part of the equation.

12:05So, it will turn into the negative sign.

12:08If you are going to use the quotient laws of logarithm.

12:13Now, log y is equal to 1 bar.

12:16Bar 1 plus 0.8312.

12:19Split this one.

12:200.09547.

12:22Thus, again split this one.

12:24This minus and this minus turns into positive 2 minus.

12:27This plus into minus turns into negative 0.3692.

12:33Log y is equal to 1 plus.

12:37By adding this one and this one.

12:391.4167 and 2.4167.

12:43Taking antilog of both sides.

12:45We will get y is equal to 251.

12:49And you will check this.

12:520.41.

12:54Guess 6.

12:56Column 6 and again column 7.

12:58You will get this value 251.

13:00This is our answer.

13:02Now, we are move to the equation number 4.

13:05Part 4 of the equation number 1.

13:07Under 5th square root 2.709.

13:13Into 7th square root 1.239.

13:17Again, 2 rules are involved in this equation.

13:23Disease rule and product rule.

13:27Let y is equal to 5th square root 2.709.

13:31Into 7th square root 1.239.

13:34Is equal to 2.709 raised to the power of 1 by 5.

13:39Into 1.239 raised to the power of 1 by 7.

13:44What I have done here.

13:45I have removed the square root sign.

13:47And turned it to the power.

13:51Taking log of both sides.

13:52Log y is equal to log 2.709 raised to the power of 1 by 5.

13:56Into 1.239 raised to the power of 1 by 7.

13:59Applying product law of logarithm.

14:07Log y is equal to log 2.709 raised to the power of 1 by 5.

14:10Plus log 1.239 raised to the power of 1 by 7.

14:13Now, applying disease rule of logarithms.

14:16This power becomes coefficient of this log number.

14:191 by 5 log 2.709.

14:22Plus 1 by 7 into log 1.239.

14:27Using log tables.

14:29Getting the log values of the numbers.

14:31Log 1 by 5 is equal to 4.314 plus 1.4.

14:35Plus 1 by 7 into 0.0899 plus 32.

14:41You can use decimal as well here.

14:45But both places.

14:470.4314 plus 0.0014.

14:51So, we will get 0.4328.

14:54And 0.0931.

14:56Keeping the coefficient same.

14:59Now, dividing this element by 5.

15:02And this element by 7.

15:04We will get 0.0856.

15:06Plus 0.13286.

15:10By adding up them.

15:11We will get 0.0999999.

15:14Taking antilog of both sides.

15:16Log there.

15:17Statistic is 0.

15:19So, we will turn into the 1.

15:21By increasing its value by 1.

15:230 plus 1 is equal to 1.

15:25So, 1, 2, 5, 6.

15:27When you look.

15:280.09.

15:29And guess 9.

15:30Under column 9.

15:31And then again 9.

15:33You will get 1, 2, 5, 9.

15:35Statistic is 1.

15:36So, we will move from left to right.

15:38One digit.

15:391.259 to place decimal.

15:42This is our answer.

15:44So, remaining two parts.

15:47And the other questions.

15:48We will do in the next video.

15:50I hope you will find this video useful.

15:52If you find useful.

15:54Please hit the like button.

15:55And share with your friends.

15:56Thanks for watching.

15:57Assalam-o-Alaikum.

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