Simplify log2x + log3x2

Question

goformit100 · Answer

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anonymous · Answer

So you want to simplify:

$$\log(2x) + \log(3x ^{2})$$

anonymous · Answer

Do you remember any of the rules for logarithms?

anonymous · Answer

Like how:

log(ab) = log(a) + log(b)
?

anonymous · Answer

Which also implies that:

$$\log(x ^{n}) = n*\log(x)$$

anonymous · Answer

But do you know what "x" is equal to?

anonymous · Answer

no?

anonymous · Answer

You said it was:

$$\log(2x) + \log(3x^{2}) $$

right? Well, you CAN simplify that expression. But, unless you know what "x" is equal to (or, what the entire expression is equal to) you will still have the "x" term somewhere in your result.

anonymous · Answer

It's for a multiple choice question and they all have an X in the answer. But I wanna now how to solve the question rather than just have the answer.

anonymous · Answer

first, look at that first rule I mentioned (i.e. that log(ab) = log(a) + log(b) ).

anonymous · Answer

That means that when you see something like:

log(2x)

You can immediately break that down into:
log(2) + log(x)

anonymous · Answer

would it be log5X^2

anonymous · Answer

Quick question: Do the multiple choice questions look like "log(a) + b*log(x)" or is there just one "log"?

anonymous · Answer

there are two logs

anonymous · Answer

$$\log2x + \log3x ^{2}$$

anonymous · Answer

Sorry, I meant the answers--do they feature two logs or one?

anonymous · Answer

no, just one.

anonymous · Answer

First, because:
log(a) + log(b) = log(a*b)

That means that:
log(2x) + log(3x^2) = 
$$\log( 2x* 3x ^{2})$$

anonymous · Answer

You with me so far?

anonymous · Answer

yeah

anonymous · Answer

log6$$\log6x ^{2}$$

anonymous · Answer

Wait, you're forgetting one of the "x"s

anonymous · Answer

Because you're multiplying "2x" and "3x^2", right?

anonymous · Answer

oh okay, so add the other x to the power?

$$\log6x ^{3}$$

anonymous · Answer

Yeah, you got it. Because

2x * 3x^2=
$$6x ^{3}$$

anonymous · Answer

Also, as an aside, you can also rewrite it as:

$$\log(6x ^{3}) = \log(6) + 3*\log(x)$$

anonymous · Answer

(Sometimes in math it's more helpful to separate the constants from the variables as well as to get rid of the exponents)

anonymous · Answer

Makes more sense now.

Thanks for help

anonymous · Answer

Ok, glad it's making sense. Good luck!