use the properties of logarithms to simplify and solve

[mirandaemalee]

Please help! I have tried and tried to figure out this question and I cannot!

log_3(6^3*9^6)

if anyone could help me with this question it would be greatly appreciated! I know all the other questions I have done it comes out something like 3log(2)+log(3)+15 or something like that.

 

[DrPhil]

Please help! I have tried and tried to figure out this question and I cannot!

log_3(6^3*9^6)

if anyone could help me with this question it would be greatly appreciated! I know all the other questions I have done it comes out something like 3log(2)+log(3)+15 or something like that.

I assume that "log_3" means "logarithm to the base 3".
That means, "What power of 3 will be equal to the expression?"

Your first step for simplifying the expression is to factor out all powers of 3. For instance, 6^3 = (2*3)^3 = 2^3 * 3^3
What is the total power of 3? Is that where your 15 came from?

Next, remember that the logarithm of a power is the power times the logarithm of the base.
A very important rule is that the logarithm of the base is always 1: log_3(3) = 1.
The other rule you will need is that the logarithm of a product is the SUM of the logs.

Try using these rules, and then show us again what you got. Some of your answer is correct.