solve the problem

Question

if 4^-x = 1/6, what does 16^x equal?

Answer 1

Nadia gave you a correct solution using logarithms.  Here is another way to solve the problem without using logarithms:

 

4^-x = 1/6

 

4^x = 6

 

16^x = [(4)(4)]^x = 4^x 4^x = (6)(6) = 36

 

The answer is the same; just another way to solve the problem.

Answer 2

4^-x = 1/6, what does 16x equal

 

1/4^x = 1/6

 

6 = 4^x

 

take log of both sides

 

log 6 = log 4^x

log 6= x log 4

 

log 6/log 4 = x

 

1.2925 = x

 

16^x = 16^1.2925 = 36