SImplifying logarithmic functions

[j9mom]

1. Homework Statement [/

Simplify: log base 2 x^2*y^3

Homework Equations

I know that log base 2 x^2 * y^3 is log base 2 x^2 + log base 2 y^3

The Attempt at a Solution

Here is what I thought:

2 log base 2 x + 3 log base 2 y But that does not seem to be simplified, it seems to be more complicated. Is there something else I should have done?

 

[Dick]

1. Homework Statement [/

Simplify: log base 2 x^2*y^3

Homework Equations

I know that log base 2 x^2 * y^3 is log base 2 x^2 + log base 2 y^3

The Attempt at a Solution

Here is what I thought:

2 log base 2 x + 3 log base 2 y But that does not seem to be simplified, it seems to be more complicated. Is there something else I should have done?

No, I don't think so. That looks correct and I think it's what they want. Instead of
"simplify" they probably should have said "express $log_2 (x^2 y^3)$ in terms of $log_2 x$ and $log_2 y$".

 

[Mentallic]

Don't be surprised if in the very next question they ask you simplify

$$3\log_2{x}-2\log_2{y}$$
or something equivalent, and you're expected to produce the result

$$\log_2{\frac{x^3}{y^2}}$$

Just keep in mind that simplify in this context usually means to take it from one extreme to the other. Leaving the answer to your question "in between" the two extremes at $\log_2{x^2}+\log_2{y^3}$ would be incorrect.