Ex 3.4 Solution-Class 9th math-Logrithms-Q 2 and 3-FBISE

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Transcript

00:00In today video we are going to solve the question number 2 and question number 3 and maybe question

00:19number 4 of exercise 3.4 and this exercise is related to chapter 3 of math of 9th class

00:28which is related to FBISC system and it means Federal Board Education System. So let's start

00:36reading the question then we will move to the solution.

00:41Question number 2, a gas is expanding according to the law P into V raised to power n is equal

00:46to C. Here P is equal to pressure, V is equal to volume and n may be some fraction value

00:53n is equal to C. Find C when P is equal to 80 and V is equal to 3.1 and n is equal to

01:015 by 4. Solution, C is equal to PV raised to power n by putting values of PV and n in

01:11above equation C is equal to 80 into 3 into 1 raised to power 5 by 4 taking log of both

01:19sides log of C is equal to log of parenthesis star 80 into 3.1 raised to power 5 by 4.

01:26Here I am going to apply the product law of logarithm in which we are going to turn multiplication

01:33into addition form. So look at this, this X multiplication turns into the positive sign.

01:52So now in next step you are going to go to the log tables where you will see 80 values

02:03in 0 column and this value is 1.9031. Here I have relied on the indices law of logarithm

02:13where the power becomes the coefficient or multiplication of the value log 3.1. So look

02:21at this 3.1 means 31 values in log table under column 0 so you will get 0.4914. So log C is

02:34equal to 1.9031 plus you will multiply this factor with this one. Either you will multiply

02:425 with this element 0.4914 and divide by 4 you will get this 0.6143. By adding that one

02:50we will get log C is equal to 2.5173. Now we want to get the value of C so in order to get

02:58this one you need to take the antilog of both sides. So antilog of log of C is equal to antilog

03:04of 2.5174. So C is equal to look 25 and now this time we are going to use antilog table.

03:15Look 25 or 0.25 under column 1 and 7. So you will get this value 3289 plus 3 and this 3 is

03:26available under column 7 of the third portion of this table 3. So the value C is equal to 3292

03:36is equal to 329.2 and this will be look at this statistics of this number is 2 so you will add

03:471 is become is equal to 3. So 329 start from left to right after counting 3 digits you will place

03:55decimal 329.2 this is our answer. Now move to the question number 3. Here is a statement the

04:03formula P is equal to 90 into 5 raised to power minus Q by 10 applies to the demand of a product.

04:10This is a demand function of a product sorry price function of a product where Q is the number of

04:17units and P is the price of the one unit. How many units will be demanded if the unit price is

04:23rupees 18. Before proceeding I am going to tell you that I have solved this question from the

04:29two methods. So we will discuss both methods in this in the solution of this question.

04:35Solution P raised to power 90 into 5 raised to power minus Q by 10 taking log on both sides log

04:4118.00 is equal to log 90 into 5 raised to power minus Q by 10. Using the log table I will get

04:50this value 1.2553. Remember that here by inspection method the statistics of this number is 1

04:59because how many digits are there before decimals 2, 2 minus 1, 1 catechistic. Now after that you

05:06will see 18 and get 0 you will get 1.2553 value is equal to log 90 and plus minus Q by 10 raised

05:16to power log 5. You have noticed that this multiplication sign turns into positive which

05:23means that we have applied product law of logarithm. After that you will see that this

05:28quotient exponent becomes coefficient or multiplication of this number. So here I

05:38apply the and this is the of logarithm 1.2553 is equal to look at this again we have 2 digits 2

05:45minus 1 catechistic is 1 point look 90 under 0 column 9542 plus minus Q by 10 0.6990 the value

05:58of log 5 is equal to 0.6990 if you look at log table. Now look at this I have divide this number

06:10by 10 so you notice that now this become 0.0699 is as you know that minus 2 is already multiplied

06:19by this number is equal to 1.2553 minus 1.9544

06:40okay minus 1.9542 this positive sign turns into negative and when you shift this from right to

06:51left side but here you see that it is on right side because we keep element as it is by changing

06:58their position minus Q into 0.0699 is equal to minus 0.699 and 989 this minus is cancelled by

07:07this minus Q is equal to 0.699 divided by 0.0699 is equal to 9.9986 is equal to 10 units. Now we

07:18will solve this question by another method which is labeled as method 2 P is equal to 90 into 5

07:25raised to power minus Q by 10 18 is equal to 90 into or multiplied by 5 raised to power minus Q by

07:3610 dividing both sides by 18 we will get 1 is equal to 5 into 5 raised to power minus Q by 10

07:45taking log on both sides log 1 is equal to log 5 plus log 5 raised to power minus Q raised to

07:52power 10 log of 1 is equal to 0 is equal to log 5 minus this exponent becomes the coefficient of

08:00this number log 5 minus Q by 10 into log into 5 and Q by 10 Q by 10 into log of x is equal to

08:12log 5 when we will shift this one on the left hand side this negative sign becomes positive

08:19log 5 dividing both sides by log 5 Q by 10 into log 5 into 1 by log 5 dividing by this

08:26is equal to log 5 into 1 divided by log 5 this log 5 is cancelled by this one and this one

08:34by this one Q by 10 is equal to 1 and Q is equal to 10 units this is the answer

08:43I hope you will find this video useful if you have any question or query about the

08:50solution of these two questions you can ask me in the comment section thanks for watching

08:56assalamu alaikum

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