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Use the logarithm identities to obtain the missing quantity:logb(p) logb(q) logb(r) logbNeed Help?Read It~M1 points WaneFMAC7 0.8.032.Letlog(2) andlog(5) Use the l...

Question

Use the logarithm identities to obtain the missing quantity:logb(p) logb(q) logb(r) logbNeed Help?Read It~M1 points WaneFMAC7 0.8.032.Letlog(2) andlog(5) Use the logarithm identities to express the given quantity in terms of a and €.log(20)Need Help?Read kt

Use the logarithm identities to obtain the missing quantity: logb(p) logb(q) logb(r) logb Need Help? Read It ~M1 points WaneFMAC7 0.8.032. Let log(2) and log(5) Use the logarithm identities to express the given quantity in terms of a and €. log(20) Need Help? Read kt



Answers

Use the logarithm identities to obtain the missing quantity. $4 \log _{b} p-3 \log _{b} q-2 \log _{b} r=\log _{b}$

In this problem, we're being asked to rewrite to give an expression as a single log by using some of our logarithmic identities. Well, the first thing I noticed is that both of our expressions has a coefficient in front of the long term. Well, one of our properties of logs says that we have a coefficient A getting multiplied by log based vfx or I'll use Y in this case because X is in the problem, we can rewrite this as log base B of Y to the power. So let's first apply this rule to our both of our expressions. So in other words we can rewrite X log base B of two as log base B of two to the X power. We'll bring down a minus sign. And for our second expression we can rewrite to log base B of X as log base B of X square. Perfect. So now we just have to combine these two expressions. We'll notice they're getting subtracted from one another. So another one of our log arrhythmic identities says that if we have log base B of Y getting subtracted by log base B of Z as a single log. This would be log base B of Y divided by C. So in other words, to combine these two expressions, we're gonna divide to to the X by X square. So we can rewrite this as log base B A. Chew to the X divided by X squared. And we can't simplify that expression. Perfect. Now we have it as a single log so we can go back and fill in our blank. It would be to to the X divided by X squared.

So in this problem we're being asked to fill in the blank. So we have blog basically of 3 -3 times the log base b of two. Equal to the log basically a blank. So we're gonna use our longer ethnic identities in order to solve this problem. So the first thing I want to do is I want to focus in on our second long term here. And I do this because it has a coefficient. Well one of our logarithmic properties says that if we have a coefficient multiplied by log base B of X. This is equal to log base B of X to the A. Power. So in this case a with equal to three And Act with Equal to two. So if we substitute this in, we'll bring down our original expression log base B of three minus we can write rewrite our second logarithmic expression as log base B of two to the third power. Well 2 to the third power. That's simply just eight. So that leaves us with log base B of three minus log base B of a. Well now we're subtracting these two logs with the same base. Another one of our properties says if we have log base B of X and we subtracted by log base B. A. Y. This is equal to log base B of X divided by Y. So in this case X would be three. And why would be eight? So if we apply this to our problem that means we would have log base B of three. Aug. And now we've written it as a single log so our final answer to fill in the blank would be 3/8.

And this problem we're being asked to fill in the blank. So the problem reads that we have log base B of three minus log base B of four is equal to log Base B A blank. Well, in order to solve this problem, we're going to have to use our log arrhythmic identities. Notice that on the left hand side we have two logs with the same base that are getting subtracted from one another. Well, one of our log aerobic identities says that if we have log base B of X and we subtracted by log base B A. Y. This would be equal to long based B of X divided by Y. So no, that's in order to use this property, both of our logs have to have the same base. Which in our problem we do, they're both based B. So all we need to do is divide their two expressions. In other words, we'll just need to divide 3x4. Well three divided by four is simply just three. Fours. Perfect. Now we filled in the blank. So log base through three minus log base B. A four is equal to log base B of three. Force

In this problem we're being asked to fill in the blank. So we have log base B. Of three plus log base B of two minus log base B of seven. Equal to log base B A blank. Well, in order to solve this problem, we're gonna have to use our log arrhythmic identities. So let's start by going from left to right. We look at our first two terms. Well we're adding these two terms that have the same base. Well, one of our log arrhythmic identities says that if we have log base B effects and we added to log basically a Y. It's equal to log base B of X times Y. So if we apply this to our problem because they have the same base to write them as a single log we simply need to multiply three times two which is equal to six. Which means we'll have log base B of six And then we'll bring down the rest log base B of seven. Well now we're subtracting these two logs well another identity says if we have log base B of X minus log base B of Y, this is equal to log base B of X divided by Y. So in this case we're going to have log base B. And then when we divide six by seven, that's just six sevens. Perfect. So now we can fill in the blank. Our final answer would be six sevens


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