Math Help - logs?

1. logs?

My teacher gave these two log questions to me, and I don't know how to do them. If someone could explain their answer it would help me out greatly.

a) log'16 2 ("log subscript 16, 2")
b) log'2 2"9 ("log subscript 2, 2 to the power of 9")

Is there a program that will let me paste equations into the thread?

2. What do you think 'log' is and/or does? Do you know the definition?

3. Log means what does the base needs to be raised to, to give your result?

Thus,
$\log_{2} 16$
Means what does 2 have to be raised to to give 16? The answer is 4. Thus,
$\log_2 16 = 4$

4. I understand the definition. and I know that log(subscript 2) 16=4. I was just stuck with:

a)log(subscript 16) 2=? , and
b)log(subscript2) 2"(to power 9)=?

-so A) is what do you raise 16 to, to get 2
- and b) is what do you raise 2 to, to get 2 to the power 9? (I think)

5. Originally Posted by math619
I understand the definition. and I know that log(subscript 2) 16=4. I was just stuck with:

a)log(subscript 16) 2=? , and
We need that,
$16^x = 2$
$(2^4)^x=2$
$2^{4x}=2^1$
$4x=1$
$x=1/4$
b)log(subscript2) 2"(to power 9)=?
$2^x=2^9$
$x=9$

6. Have you seen the following property?

$\log _a b = \frac{1}{{\log _b a}}$

7. No, I have not seen that before.

so, if I have:

a)log (subscript 7) 7

that would equal 1?

AND

b)

that would equal 19?