SOLUTION: Express the following as an equivalent expression using the individual logarithms of w, x, y, and z. Log a[ (x y^2 w ) / z^2 ]

Question 225278: Express the following as an equivalent expression using the individual logarithms of w, x, y, and z.
Log a[ (x y^2 w ) / z^2 ]

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
So the problem is, in other words, take the argument of and separate all the parts into separate logarithms. To do this we need to know some of the basic properties of logarithms, especially those that allow you to remove, in effect, parts of the arguments. These properties are:

This allows us to remove an exponent in the argument and move it in front of the log as a coefficient.
This allows us to split the log of any product into the sum of the logs of the factors.
This allows us to split the log of any quotient/fraction/division into the difference of the logs of the dividend/numerator and divisor/denominator.

NOTE: All these properties can also be used in reverse. For example the first property above can be used to move a coefficient into the argument as an exponent. But we will no need to use them that way for this problem since we are dismantling an argument, not building one.

Now that we have our properties lined up, let's start taking apart the argument of . The order in which we do things is not important as long as your Algebra and your use of the properties is correct. I am going to start by using the third property to split apart the fraction in the argument:

Next I'll use the second property above to split apart all the products:

(Note: These last two steps could have been done in one step.)
And finally I'll use the first property to remove the exponents:

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