SOLUTION: expand each logarithiam log4 a^4/b^3 log3 sqrt 2x log3 x^2y^3

Question 411048: expand each logarithiam
log4 a^4/b^3
log3 sqrt 2x
log3 x^2y^3
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Please post 1 (maybe 2) problems in each post. Posting three problems may be the reason that you have not received a response prior to this. I will do one and perhaps that will help you figure out the others. (If not, then repost them.)

There are three properties of logarithms that are used when "expanding" logarithms:

which shows us how to write the log of a product as the sum of the logs of the factors (and vice versa).
which shows us how to write the log of a quotient as the difference of the logs of the numerator and denominator (and vice versa).
which shows us how to write the log of a power as the exponent times the log of the base of the exponential argument (and vice versa).

The argument is a quotient. So we will use the second property to get:

Both of these logs are logs of a power. So we will use the third property on both to get:

When the arguments are no longer a product, quotient or power, then the expression is fully "expanded". So we are finished.

Some hints for :

Use the fact that square roots are exponents of 1/2 to rewrite as .
Eventually you will be using the first property on . When you replace this with what the first property shows you, put the new expression in parentheses when you substitute. I think you'll see why once you do this.

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