Quandaries
and Queries 

Who is asking: Teacher Level: Secondary Question: 2^{10} = 1/2^{x}  1 If you look to get to a common base I'm not sure how to deal with the negative in front of the one half. Thanks 

Hi Randy, The negative in front of the onehalf is a problem. If a is any positive real number and b is any real number then a^{b} is positive. Hence the left side of the equation
is positive and the right side is negative. Thus there is no x that makes the equation valid so there is no solution. Harley Randy wrote back.
Randy, There should be a bracket around the 1/2 as it is the common ratio. You are starting at 2^{5} and succesively multiplying by 1/2 andyou want to know how many times you have to do this to get to 1/32 = 1/2^{5}.
Equivalently ,
so k=10 and the term you're after is the 11th term. Penny 

