Expert: Bobby Soltani - 2/20/2005

Question
hi there, I am not really sure how to do indices and whether should I ask this question under algebra, but I will just ask you a question.

If 3^x = y and 2^x= z , express the following in terms of y or/and z.

a) 6^x-1   b)9^-x X 12^x


for a)how do i make it contain 3^x? nothing to the power of something gives 6...

Answer
Hi Joe,

For these problems, you need to recognize the following:

6^x = (2*3)^x = 2^x * 3^x

So, for part a:

6^x - 1 = (2*3)^x - 1 = 2^x * 3^x - 1 = zy - 1

For part b:

9^-x * 12^x = (1/(9^x))12^x = (12^x)/(9^x)
=(3^x * 4^x)/(3^x * 3^x)
the 3^x on top cancels with one of the 3^x on bottom
= (4^x)/(3^x)
= (2^x * 2^x)/(3^x)
= (z * z)/y
= (z^2)/y

Let me know if you have any questions.

Bobby