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EtulualEIoltenl (sinfik)a:Find r(r) given that af) = | + F1rto) = ZJand r(o)...

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EtulualEIoltenl (sinfik)a:Find r(r) given that af) = | + F1rto) = ZJand r(o)

EtulualE Ioltenl (sinfi k)a: Find r(r) given that af) = | + F1rto) = ZJand r(o)



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Obtain (a) the $K_{b}$ value for $\mathrm{ClO}^{-} ;$ (b) the $K_{a}$ value for $\mathrm{NH}_{3} \mathrm{OH}^{+}$ (hydroxylammonium ion).

So in the given question we are told that if I mean Times killed Times R. is equal to one. Then what is the value of dog? Uh Are you prepared a log a log with base R. Q. P. Bless Margaret based R. P. Of queues plus log with they speak you of art. So what we can write from this relation is that we can write B. Is equal to one by cuba. Are won by our cue and Cuba sequel to one by R. P. And are the sequel to one by teaching. So now on substituting this in the expression during the question We have one x 1. Law with Base Our Cube of one by argue plus love with base R. P. Of one by R. P. Plus log with base dog with they speak you of one by picking Which we can further simplify and write us log with base our cube of our Q. to the power -1. Let's love with base arty of RT to the power -1 plus. Love with PQ with base PQ of P. Q. To the power minus one. Now we can use a property which says along with base A. Of A. To the power and is equal to. And so over here we have log with base RQ of our Q. To the power my minus one. Which would give us the value of this law with them as minus one. And similarly we would have minus one for the values of these expressions. These logarithms also so minus one plus minus one plus minus one Is Equal Group -1. So -3 is a required answer. I hope you understood the mattered. Thank you.

As the value okay is given us to. So first we will multiply it with given metrics is on the value of metrics A is my last one. Do B and four simply multiply the skill er going today with tricks we will get. Are you still 46 and eight? Now we have to find its determinant. So let's write it and let determinant form simply by cross multiplying the elements and putting the separate creature sign in the middle. We will get the answer after depending minus two multiplied with eight and minus for IHS multiplied with six, it's equal to minus 16 and minus 24. I was 16 and minus 24 equals two minus what it is the value off the left hand side now.

All right. We want to verify their identity for a constant K and a matrix. A determinant of K is equal to K to the end and is the number of rows and the determinant of a. For a given by rose to two and five negative two and K equals negative four. So to start off, let's take the determinant or rather compute the values on either side of this equation and then see whether or not the equal to determine if we can verify this formula. So first determine of K. A. On the left. K. A is simply the constant times every single entry in the matrix. Okay. Is negative eight, negative eight and negative 28. The determinant of K. A is in the simple determinant formula negative eight times eight minus negative times negative 20 or negative 64 minutes 1 60 equals negative 224. So we have the left side of the equation. Let's now take A. And determining a. K. And determine A is equal to negative four squared times the determinant A, which is simply two times negative two minus two times five, negative four square to 16 in the content of the season negative four minus 10. So we have negative 16, or rather 16 times negative 14, which is negative 24 which shows because the left and right to equal the determinant K is equal to K and determine A.

So here we have been given that B. Is equal to Log off A. two. Base to a. Q. Is equal to log off to a. To base three. And our is given as log off 3 8 to base for a. And we need to figure out the value of You are Times 2 -7. So here we expand this it would be to Q. R minus speak you are. So we are observing that cure is the term which is observed in both of these terms here. So we will first figure out the value of Q. Into our. So that would be equal to log off to eight to base three A. Times log off 3 8 to base for a. So here we will use the idea that log off a two base B is equal to log off one by log of be too busy. So in that Since this cure would become log off to 8 to base three times we will use that identity to change this term. So it will be won by log off 48 to Base three. So this will become Q. R. Is equal to Log of 282-based 3 a Over log off 48 to Base three. So here the bases are same for the numerator and denominator. So here this gives us Log of 2 8 to base for a. So let's keep this aside And now we can figure out the required thing here secure into two minus B. That will be equal to two q. R minus you are into P. So this would be equal to two times. We'll put the value of cuBA. That we got an equation one. So log off 2 8 to base for a minus log off 28 to base for eight times p. And he was given to assess Log of 8 to based away. So here again in the second term we use this identity here and now we change so after changing we get this as log off 2 8 to base for a. And this too will be squaring this term because that's again an identity that log of X rays to M is mm times log X. And the second term we will change this log off 82-based away as one by log off to a two base A. Here or let's make this to a same because here the power and this basis same. So we will change this Log of two A 2 base for a only. So it will be one by log off 4 8 to base to a. And we'll keep this As it is log of 8 to base to it. So now this log of eight to base two divided by log of 42 based away. That will be log off 8 to base for a. And the rest is as it is so to a square that is for a square to base 40. So here we again use the identity. We know that log I am minus log and his log mm. Bye. And so here this will become log off for a square Over a two base for a. So that will be log off for E to base for A. And here this is equal to one because log of eight to base, He is always one.


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