Expand formula log easily

Aug 6th, 2022
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How to expand formula log

4.8 out of 5
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in this lesson were going to take a single log and expand it into a sum or difference of logs so before we do that lets just review some basic properties as you mentioned before log of a to the n is equivalent to n log a and log a times b you can expand it as log a plus log b and log a divided by b is going to be log a minus log b now because a is on the top its going to have a positive sign next to it b is on the bottom so it has a negative sign next to it so consider this problem log x y divided by z go ahead and expand the expression x and y are both on top so its going to be positive log x plus log y z is on the bottom so its going to be minus log z try this one log a squared b to the third c to the fourth d to the fifth go ahead and expand it so a and b are both on top so its going to be positive log a squared plus log b to the third c and d are on the bottom so its going to have a negative sign in front of it so its going to be minus log c to the fourth minus log d to th

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0:13 5:41 100 Write a Logarithmic Expression in Expanded Form (4.4) - YouTube YouTube Start of suggested clip End of suggested clip So first thing I would do is say log base 4 of 5 plus log base 4 of X. And then of course Ive got aMoreSo first thing I would do is say log base 4 of 5 plus log base 4 of X. And then of course Ive got a Y Z on the bottom which means both of those will be subtracted. So log base 4 of Y.
0:13 5:41 So first thing I would do is say log base 4 of 5 plus log base 4 of X. And then of course Ive got aMoreSo first thing I would do is say log base 4 of 5 plus log base 4 of X. And then of course Ive got a Y Z on the bottom which means both of those will be subtracted. So log base 4 of Y.
1:17 5:40 Expanding logarithms - Using the properties of logarithms - YouTube YouTube Start of suggested clip End of suggested clip And basically the idea is is that if you see an exponent on top of a log. You can move that exponentMoreAnd basically the idea is is that if you see an exponent on top of a log. You can move that exponent to the front and multiply it with the log and it is exactly equal you have not changed the log.
Fact: The power series expansion of logz about z0 has radius of convergence R = |z0|, for z0 = 0, and any branch of logz. Proof. The radius of convergence for logz about z0 is the same as the radius of convergence for its derivative, (logz) = z1. The function z1 is analytic on C\{0} D|z0|(z0).
0:31 3:21 How to Expand a Logarithm : Logarithms , Lesson 10 - YouTube YouTube Start of suggested clip End of suggested clip So lets go ahead and write that out here so log base 3 of all this stuff is equal to log base 3 ofMoreSo lets go ahead and write that out here so log base 3 of all this stuff is equal to log base 3 of the numerator. So our numerators was on top x squared + y to the 3rd n.
The difference between log and ln is that log is defined for base 10 and ln is denoted for base e. For example, log of base 2 is represented as log2 and log of base e, i.e. loge = ln (natural log).
The expansion of log(1+x) is a series of terms that gets closer and closer to x as the number of terms gets larger. This expansion can be used to calculate the value of x when given a logarithm. log (1+x)=x- ((x^2)/2)+((x^3)/3)-((x^4)/4)+
0:39 3:20 Rewriting Logs in Exponential Form - YouTube YouTube Start of suggested clip End of suggested clip Example this is log base b of x equals n. So the inverse of taking the log base b is to exponentiateMoreExample this is log base b of x equals n. So the inverse of taking the log base b is to exponentiate both sides using base B.
1) Multiplication inside the log can be turned into addition outside the log, and vice versa. 2) Division inside the log can be turned into subtraction outside the log, and vice versa. 3) An exponent on everything inside a log can be moved out front as a multiplier, and vice versa.
0:08 1:27 Expand: log(32^3) - YouTube YouTube Start of suggested clip End of suggested clip So i can expand that to be edition. So i the log. Of 3 plus log of 2 to the third power. Okay.MoreSo i can expand that to be edition. So i the log. Of 3 plus log of 2 to the third power. Okay.

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