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in this video were going to talk about how to find the indefinite integral of logarithmic functions like this one what is the integral of log base 4 of x it turns out that there is a formula you could use the integral of log base a of u d u is equal to u times log base a u divided by e where e is a constant 2.7182818 and that number divided by u prime now this works if that is if u is a linear function so this could be like 5x x 3x plus 4 and so forth if u is equal to x cubed plus 9 thats not a linear function its not going to work so just keep that in mind so in this example we can see that u is equal to x a is four and u prime the derivative of x is one so the answer is going to be u x log base a or four of u over e so thats going to be x over e divided by u prime which is 1. and so we dont need to write one and then plus the constant of integration so this is the integral of log base 4 of x so thats the simplest way to get the answer using the formula but lets talk about how

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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.

For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2. because. 102 = 100. This is an example of a base-ten logarithm. log2 8 = 3. because. 23 = 8. In general, you write log followed by the base number as a subscript. log. log a = r. ln. ln a = r.

0:36 6:08 Logarithms introduction - Solving Logs without a calculator - YouTube YouTube Start of suggested clip End of suggested clip Without using a calculator. We need to make the number inside of the parenthesis. Its number 16. WeMoreWithout using a calculator. We need to make the number inside of the parenthesis. Its number 16. We need to make it exactly the same as the base. So were going to change this number 16.

The log of a sum is NOT the sum of the logs. The sum of the logs is the log of the product. The log of a sum cannot be simplified.

0:36 6:08 Logarithms introduction - Solving Logs without a calculator - YouTube YouTube Start of suggested clip End of suggested clip So what we have to do is add an exponent on top of this 2 in the parenthesis. And make it equal toMoreSo what we have to do is add an exponent on top of this 2 in the parenthesis. And make it equal to 16. And we know that 2 to the 4th power 2 times 2 times 2 times 2 is equal to 16.

We can easily calculate that ln 10 = 2.302585093 or 2.303 and log 10 = 1. So, the number has to be 2.303.CALCULATIONS INVOLVING LOGARITHMS. Common LogarithmNatural Logarithmlog x/y = log x - log yln x/y = ln x - ln ylog xy = y log xln xy = y ln xlog = log x1/y = (1/y )log xln = ln x1/y =(1/y)ln x1 more row

0:51 3:07 Logarithms : Expanding and Combining , Example 3 - YouTube YouTube Start of suggested clip End of suggested clip We could write our next term as the natural logarithm of X cubed. Plus five raised to the 13th.MoreWe could write our next term as the natural logarithm of X cubed. Plus five raised to the 13th. Power. And then we would have minus the natural logarithm of X plus one raised to the one-half.

2:42 7:26 Combining Logarithmic Expressions - YouTube YouTube Start of suggested clip End of suggested clip Right here its log base B of a product equals log base B of X plus log base B of Y. So weve gotMoreRight here its log base B of a product equals log base B of X plus log base B of Y. So weve got the sum of logs the bases have to match up the bases have to match up in order for me to combine them.

ln(x)(y) = ln(x) + ln(y) ln(x)(y) = ln(x) + ln(y) The natural log of the multiplication of x and y is the sum of the ln of x and ln of y. Example: ln(8)(6) = ln(8) + ln(6)

0:00 1:38 How To Type Log Base In Word - YouTube YouTube Start of suggested clip End of suggested clip Type what you want for example log base 10. And then the number next method is also easy go to theMoreType what you want for example log base 10. And then the number next method is also easy go to the insert tab click on equation. Again this time you can select the option script under the script.

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