SOLUTION: Please help me solve this equation: expand log base5 of 8square root y/m

Question 405048: Please help me solve this equation: expand log base5 of 8square root y/m
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

There are three properties of logarithms that are used in these "expansion" problems:

Your logarithm's argument is the product of 8 and the square root. So we can use the first property, the one for products, to do the first expansion:

The next step is the trickiest. Remembering that a square root is the same as a power of 1/2 we can rewrite the square root. And by rewriting the argument this way we can use the third property above to expand it:

Using the third property on the second logarithm we get:

Next, since the argument of the second logarithm is now a quotient, we can use the second rule to expand it:

Note the use of parentheses! This is an excellent habit to have when substituting one expression for another, especially when the two expressions have a different number of terms. Here we are replacing a single logarithm with the difference of two logarithms (one term replaced by two terms). Without the parentheses we might not realize that the 1/2 applies to both terms! With the parentheses it should be obvious that the Distributive Property must be used:

This is the "expanded" expression, with each logarithm's argument being a simgle number or variable.
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