Discover the quickest way to Fix Sum Log For Free

Aug 6th, 2022
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How to Fix Sum Log For Free

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in this video we are going to calculate the sum of logarithms of n cubed minus 1 all divided by n q plus 1 add from n equals 2 to infinity before we move on dont forget to give a like subscribe to my channel and turn on post notifications we can show that this series indeed converges with the integral test but im just going to omit it because thats not the main thing that i would like to share about the summation so to evaluate this sum im going to rewrite that as the summation with the same starting and ending points of the logarithm of n cubed minus 1 minus the logarithm of n cubed plus 1. so just splitting the numerator and the denominator then i can factorize n cube minus 1 and n cubed plus 1. so for the first logarithm ill split it as the sum of logs of n minus 1 and n squared plus n plus 1 while for the second logarithm it will become log of n plus 1 and log of n squared minus n plus 1 is simply factorization next im going to split into two summations one dealing with the

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0:17 7:30 Expressing Log functions as a sum or a difference - YouTube YouTube Start of suggested clip End of suggested clip And were adding those two logs. Okay.MoreAnd were adding those two logs. Okay.
0:00 0:58 How to Solve a Common Logarithm: log(10) - YouTube YouTube Start of suggested clip End of suggested clip So this is equal to 1. And that actually is all there is to this problem. Large base 10 of 10 is 1.MoreSo this is equal to 1. And that actually is all there is to this problem. Large base 10 of 10 is 1. And again thats because the power of 10 is. 1.
0:25 5:03 Sum of logarithms with same base | Algebra II | Khan Academy - YouTube YouTube Start of suggested clip End of suggested clip This is equal to the logarithm base b of a plus the logarithm base b of c.MoreThis is equal to the logarithm base b of a plus the logarithm base b of c.
4:41 5:37 Expand to the sum or difference of logs - YouTube YouTube Start of suggested clip End of suggested clip So log base 3 of 9 what do I raise 3 to to get 9 that becomes a 2 were then going to add we moveMoreSo log base 3 of 9 what do I raise 3 to to get 9 that becomes a 2 were then going to add we move the power to the front for log base 3 of M power to the front minus 1/3 log base 3 of n.
0:31 11:13 rewriting as a sum or difference of logs - YouTube YouTube Start of suggested clip End of suggested clip So when I write 5x the understood operation is 5 times. X. So we just write it as ln. 5 plus ln x.MoreSo when I write 5x the understood operation is 5 times. X. So we just write it as ln. 5 plus ln x. And thats it weve written it as a sum of two logs of the same base.
To convert from exponential to logarithmic form, we follow the same steps in reverse. We identify the base b, exponent x, and output y. Then we write x=logb(y) x = l o g b ( y ) .
0:25 5:03 Sum of logarithms with same base | Algebra II | Khan Academy - YouTube YouTube Start of suggested clip End of suggested clip This is equal to the logarithm base b of a plus the logarithm base b of c.MoreThis is equal to the logarithm base b of a plus the logarithm base b of c.
Natural Logarithm of Negative Number The natural logarithm function ln(x) is defined only for x0. So the natural logarithm of a negative number is undefined.
0:09 2:21 Solving a Log Equation with a Sum - YouTube YouTube Start of suggested clip End of suggested clip So in this case we have log base 2 of X plus log base 2 of X minus 2 equals 3. Now because thoseMoreSo in this case we have log base 2 of X plus log base 2 of X minus 2 equals 3. Now because those logs have the same base we can use the fact that we have the sum of two logs.
0:09 2:21 Solving a Log Equation with a Sum - YouTube YouTube Start of suggested clip End of suggested clip So in this case we have log base 2 of X plus log base 2 of X minus 2 equals 3. Now because thoseMoreSo in this case we have log base 2 of X plus log base 2 of X minus 2 equals 3. Now because those logs have the same base we can use the fact that we have the sum of two logs.

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