please help me solve this!
Log base 2(M) + log base 2 (N)+3

Question

please help me solve this!
Log base 2(M) + log base 2 (N)+3

terenzreignz · Answer

By simplify, you mean write with just one log?

terenzreignz · Answer

*solve
rather

terenzreignz · Answer

Were that the case, use this property of logarithms....
$$\huge log_bM+log_bN=log_bMN$$

anonymous · Answer

yeah that what i mean! i got log base 2 (MN)+3
the books says log base 2 (8MN)

anonymous · Answer

im not sure where the 8 comes from!

terenzreignz · Answer

Precisely :)
You have to express 3 with a log base 2 on it.
But for now, you agree with me that
$$\huge \log_2 2 = 1$$
right?
That is to say, the exponent you raise 2 to, so that you get 2, is 1.

anonymous · Answer

Yup! I agree with the Log 22=1!

terenzreignz · Answer

Now remember this property of logarithms:
$$\huge p\log_bM=\log_bM^p$$
?

anonymous · Answer

yeah! the P gets moved to the back!

terenzreignz · Answer

Okay, so, what with
$$\huge \log_22=1$$and all, we can multiply it to 3, and it's still going to be 3...
$$\huge 3 = 3\log_22$$
Catch me so far?

anonymous · Answer

Yeah i think so! its basically like 3=(3)(1) right?

terenzreignz · Answer

That's right, so we now have
$$\huge 3=3\log_22$$
Now, we make use of this property... (otherwise, why would I bring it up? :P )
$$\huge p\log_bM=\log_bM^p$$
can you see where I'm going with this?

anonymous · Answer

yeah i think i got it now! I just didnt put them together! 
haha thanks Teren! your a beast!

terenzreignz · Answer

No problem :)