SOLUTION: how to expand ln x^3(x-2)^2/ sqrt x^2+5

Question 883007: how to expand ln x^3(x-2)^2/ sqrt x^2+5
Answer by Leaf W.(135) (Show Source): You can put this solution on YOUR website!
Hello!
***
You can use a few "logarithm rules" to expand out logarithms of any base:
1. The log of the product of two numbers is the same as adding the individual logs of each number:
2. The log of the quotient of two numbers is the same as subtracting the individual logs of each number:
3. The log of a number raised to a certain exponent is the same as the value of that exponent multiplied by the log of that number:
***
Now let us apply those rules to this case!

Use rule #2 to get rid of the division:
Use rule #1 to get rid of the multiplication:
Since taking the square root is the same thing as raising to the one-half power:
Use rule #3 to get rid of exponents:
***
Therefore, the expanded expression is
I hope this helps! =)
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