SOLUTION: log square root 100y in expanded form

Question 383943: log square root 100y in expanded form
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

To start we need to remember that a square root is the same as an exponent of 1/2. So we can rewrite your expression as:

Next we can use a property of logarithms, , to move the exponent of the argument out in front:

Next we can use another property of logarithms, , to rewrite the log of the product as the sum of the logs of the factors:

Note the use of parentheses. It is an extremely good habit to use parentheses when substituting. In this case it helps us know that the Distributive Property applies with the 1/2:

Since the base of log is 10 and since , :

which simplifies to:

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