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Because? You learn. This is Emmanuel Advice. Subscribe to the channel. Today is a video of logarithms and mathematics. We are going to solve several exercises. The objective is to use the properties of logarithms.
That is why I use this form This is the form for Manuel Assures. And here are all the formulas for logarithms. This. Is example. Number one., So, look, We have the logarithm of the square root.
It is square x. Fourth. As, you can see, the most important thing is the logarithm, but then everything has a root. You should know that a square root is always passed exponent. We will be left with the logarithm.
And in parentheses, we always transform the root. The square root is the same as a half. And inside, they remain the same be square, x 4a.
Then the first step, we convert the square root to a half the inside remained the same the headquarters house and the x. Now we are going to use another property, always. Before the general exponent, that is, the one in parentheses, a half must be passed before logarithms, These exponents must always accrue before logarithms, It is by formula, Then we bring the half to the beginning, and we will have a half left, and we write the same logarithm of squared x 4a.
So we can even remove the parentheses so that it stays that way. Now we are going to do the following. We are going to continue. This can still be converted. Now we have a logarithm, and we have a multiplication.
The c squared by the x 4a, whenever logarithms have multiplications, we must from passing them to sum from multiplying to sum. We will have two logarithms. We are going to keep this one half that no longer moves. And in a parenthesis, we put the result. Then it was this to pass it to add logarithm of the first letter is squared, plus another logarithm of the other variable a, the 4th and close the parentheses because one medium affects all of them, So finally, we apply or For another property, We lower. The parentheses by a half and, again, look at the exponents when there are exponents left, the exponents are written down at the beginning of their logarithm, Thus leaving us with the 2 logarithm of being plus the 4, the logarithm of bets, And that you are seeing a half times two logarithms of c4. Logarithm of x is the answer for this example.
Now let's go to exercise number 2. We have a logarithm now this logarithm has a small number here below it is said to be the base is logarithm base. 4Dx. Fifth and to the main zeta to 13 and look this is multiplying. We have x because by z, when you see letters together, remember that it indicates multiplication, then when multiplying they go on to add in the logarithms, this 4 is going to be kept like this logarithm base. 4 of the first letter x, fifth, plus another logarithm base, 4 of the following variable to the 10 plus and another, the basics of the base, 4 of the variable zeta. 13, remember that this is by formula.
If you are multiplying, you add them. And that each one has its logarithm and with that we check and observe well, all the variables have an exponent. So by formula, the exponents are passed before it is a logarithm, and they all have an exponent. We will have 5 logarithm base, 4 of x, plus 10 with its logarithm. 4 Bella, plus logarithm is going to be 4 dz.
And all this that you are seeing enclosed all this sum is the same as the original. But from one argument we pass to several that is the objective and let's go to finish with exercise. Number 3 in this example, number 3, we have in. This is another logarithm, but it does exactly the same thing applies to natural logarithms properties. And we have a quotient is a division or fraction XY / ml. So the main thing is this fraction.
And when this violation or dividing is passed from division to subtraction, that is to say, We will have the natural logarithms of the natural logarithm of those above minus the natural logarithm of the one below, which is why it remains so like subtraction, but. Look now here we have a multiplication, you know that when two letters together are thus joined in multiplication, both Guille and MN are as if they had a dot, they are multiplying. Then remember you have to do the following you have to separate them as much as possible. And if they are multiplying, they go on to add this. We will be left with the logarithm of x plus logarithm.
So from this multiplication, this one came out then minus, and we are going to open a parenthesis to place. The answer of this. Logarithm now it is multiplying in the logarithms, and they are multiplying. They put to add the logarithm of the first letter, m, + logarithm of the other variable that is the l and close the parentheses. We had to open it because this minus affects everything. And there are those who can do this to each variable.
They put a small parenthesis to distinguish. And for example, do not confuse the logarithms with their letter. And what you are seeing is the result for this example, number 3 using properties, Of logarithms n, Manuel consultancies, subscribe to the channel I, send you greetings from doctor.
Dated : 18-Apr-2022