SOLUTION: Solve the equation 2^(2x) - 2^(x+1)-15=0 Find the domain f(x) = log((log((x-1))))

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve the equation 2^(2x) - 2^(x+1)-15=0 Find the domain f(x) = log((log((x-1))))      Log On


   

Question 685211: Solve the equation 2^(2x) - 2^(x+1)-15=0

Find the domain f(x) = log((log((x-1))))
Answer by pmatei(79) About Me  (Show Source):
You can put this solution on YOUR website!
2%5E%282x%29+-+2%5E%28x%2B1%29-15=0+++
Re-write it as:
%282%5Ex%29%5E2+-+2%2A2%5Ex+-+15+=+0
Replace 2%5Ex+=+y
y%5E2+-+2y+-+15+=+0
Solve the quadratic in y:
%28y-5%29%28y%2B3%29=0
y+=+5 and y+=+-3
2%5Ex+=+-3 has no solution.
2%5Ex+=+5
x%2Aln%282%29+=+ln%285%29
x+=+%28ln%285%29%29%2F%28ln%282%29%29

Domain for f%28x%29=log%28%28log%28%28x-1%29%29%29%29
The argument of logarithmic function has to be a positive number.
The first log has as argument log(x-1):
log%28%28x-1%29%29%3E0
Logarithm function is positive if the argument is greater than 1. Logarithm of 1 is zero. And below 1 logarithm function is negative.
x-1%3E1
x%3E2
So the domain of f(x) is x%3E2.