Expert: Sherman D. - 4/19/2005

Question
Well the question is confusing.  Here is a problem that has an answer in the back of the book.

Rewrite the exponential expression to have the indicated base:

Question:
9^(2x),  base 3

The answer is:
3^(4x)

I don't get it.


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Followup To
Question -
I need help with a homework assignment. I am confused as to what I am supposed to do. The questions are as follows:

Rewrite the exponential expression to have the indicated base.

1) 16 raised to the 3x, base 2

2)(1/27) raised to the x, base 3

I want to learn how to solve this properly. What are the steps or rules I need to follow in order to answer these problems? I have about 10 of these to do but these two are similar to the rest of the questions in my homework. If you can help me work these, I can do the rest.


Thanks!
Answer -
are you saying

1.)
16^(3x) = 2
and
2.)
(1/27)^x = 3

if so, then

1.)
16^(3x) = 2
(2^4)^(3x) = 2^1
2^(4 * 3x) = 2^1
2^(12x) = 2^1
12x = 1
x = (1/12)

2.)
(1/27)^x = 3
(3^(-3))^x = 3^1
3^(-3x) = 3^1
-3x = 1
x = (-1/3)

if this isn't what you meant, please let me know.

for example, if you mean

1.) log(base 2)(16^(3x))
2.) log(base 3)(1/27)

then let me know if this is what you meant.

Answer
9^(2x), base 3

if by this you mean

9^(2x) = 3
(3^2)^(2x) = 3
3^(2 * 2x) = 3
3^(4x) = 3
4x = 1
x = (1/4)

and that is how they got the answer.

whenever you raise a power to a power, you have to multiply them.

give me all that you got and i should be able to help, now that i know what you mean.