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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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Expanding a Log means going from a single Log of some value to two or. more Logs. This is easily understood when you look at the Multiplication Property. Log (A*B) = Log (A) + Log (B) You begin with a single Log of (A times B) and then expand it to the sum of two individual.

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.

0:31 5:37 Expand to the sum or difference of logs - YouTube YouTube Start of suggested clip End of suggested clip I take the log of a product then I can sum two separate logs in a similar vein. If I divide. Then IMoreI take the log of a product then I can sum two separate logs in a similar vein. If I divide. Then I just get log base a of M. And log base a of n. The division to log quotient.

Algebra Examples Logarithm base 3 of 3 is 1 .

To expand logarithms, write them as a sum or difference of logarithms where the power rule is applied if necessary. Often, using the rules in the order quotient rule, product rule, and then power rule will be helpful. To simplify logarithms, write them as a single logarithm.

1:12 9:31 Expanding and Condensing Logs - YouTube YouTube Start of suggested clip End of suggested clip So now when you go from the left to the right. Thats expanding when you go from the right to theMoreSo now when you go from the left to the right. Thats expanding when you go from the right to the left thats condensing youre condensing into just one log. So lets take a look at some examples.

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.

0:08 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.

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.

Expanding a Log means going from a single Log of some value to two or. more Logs. This is easily understood when you look at the Multiplication Property. Log (A*B) = Log (A) + Log (B) You begin with a single Log of (A times B) and then expand it to the sum of two individual.

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