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How to extend equation log

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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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How do you expand a log equation?

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.

What is expanding a log?

When you are asked to expand log expressions, your goal is to express a single logarithmic expression into many individual parts or components. This process is the exact opposite of condensing logarithms because you compress a bunch of log expressions into a simpler one.

What does it mean to expand a logarithmic expression?

When you are asked to expand log expressions, your goal is to express a single logarithmic expression into many individual parts or components. This process is the exact opposite of condensing logarithms because you compress a bunch of log expressions into a simpler one.

How do you expand logs to sum or difference?

0:31 5:37 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.

How do you expand log 3?

0:08 1:27 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.

How do you expand a log with a root?

0:00 1:42 If i want to expand this logarithm expression the first thing im going to want to do is get rid ofMoreIf i want to expand this logarithm expression the first thing im going to want to do is get rid of the root. So i can rewrite. This as ln of z. Over z squared plus 1 raised to the one-half.

How do you expand log properties?

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.

How do you write a log in expanded form?

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.

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