Help with logarithms please - for those really good in math?

Question

Expand the logarithm:

log3 9x^2(x+2)^3

= log3 9 + log3 x^2 + log3 (x+2)^3 HOW DOES IT GO FROM HERE TO BELOW??

= [ 2 + 2log3 x + 3log3 (x+2)] This is the answer.


I hope you can understand this.

Answer 1

Ok so the iam going to label the parts of the quation
a) log3 9
b) log3 x^2
c) log 3 (x+2)^3

so...
a) log base 3 of 9 is 2 because 3^2=9

b) the only thing you can do with this is bring the exponent ^2 to the front making the log 2log3 x

c) again, the only thing you can do is bring the exponent of ^3 to the front which makes it 3log3 (x+2)

final equation [ 2 + 2log3 x + 3log3 (x+2)]

Answer 2

log3 9x^2(x+2)^3
= log3 9 + log3 x^2 + log3 (x+2)^3

(power comes at front)
=log3 3^2 + 2log3 x + 3log3 (x+2)
=2log3 3 + 2log3 x + 3log3 (x+2)

(log(a base) a= 1)
=2*1 + 2log3 x + 3log3 (x+2)
=2 + 2log3 x + 3log3 (x+2)

Answer 3

Make this easy on yourself: Anything in the argument that's being multiplied, make it addition, anything that's being divided, make it subtraction. Don't worry about the order...

log3 9 + log3 (x^2) + log3 (x+2)^3
= 2 + 2 log3 x + 3log3 (x+2)

The first 2 is there simply because log3 9 = 2 --> [b/c 3^2 = 9]

The other property used here is the exponent property of logs, log B^x = x*log B

Answer 4

log3 [9x²(x+2)^3]
log3 9 + log3 x² + log3 (x+2)^3

In logs you can multiply the powers.

log3 9 + 2log3 x + 3log3 (x+2)

What power do you put on the base three to get nine ? (2).

2 + 2log3 x + 3log3 (x+2)

Answer 5

Just keep the log3 rolling. In base 3, 9=2 or 3^2
In any valid log base, log x^2 = 2 log x.
Same deal for the last term.
So there you are.

Answer 6

I understand...
log3 (9)=log3 (3^2)=2
loga (x)^b=b loga x
so log3 (x)^2=2 log3 x
and log3 (x+2)^3=3 log3 (x+2)
the answer is 2+2log3 x+3 log3 (x+2)
hope that helps

Answer 7

Log's are sort of the inverse of powers.

So, taking a look at each piece of your equation

1st Addend:
you get log 3 9 = log 3 (3^2), which means, what is the power of base 3 that I can use to get 9, which in this case, is 2!

The rest don't break down, quite as obvious, but they are really all the same pattern

2nd addend:
log 3 x^2, is similar to above, what is the power of base 3 that I can use to get to x^2. Well, since we already have the 2 factored out, we can simply use it to multiply with, so we end up with:
2 log 3 (x)

3rd Addend:
log 3 (x+2)^3
So I hope you see the pattern now...

= 3 log 3 (x+2)

That's it!

Answer 8

dont do homework u ugly *****