Expand log easily

Aug 6th, 2022
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How to expand 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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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.
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.
0:13 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.
How to Write in Logarithmic Form The logarithmic form is written as loga(c)=b. The purpose of the logarithmic form is to calculate exponents and solve exponential equations. Any exponential equation of the form ab=c can be written in logarithmic form using loga(c)=b.
Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8. In the same fashion, since 102 = 100, then 2 = log10 100.
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.
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.
0:03 1:03 Expanding logarithmic expressions - YouTube YouTube Start of suggested clip End of suggested clip If I have what Im taking my longer than raised to a power I can rewrite that in front to myMoreIf I have what Im taking my longer than raised to a power I can rewrite that in front to my logarithm. So therefore this would be three halves Ln of X.

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