SOLUTION: What does x equal in the problem... 4^(x+1) = (1/2)^(-x)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: What does x equal in the problem... 4^(x+1) = (1/2)^(-x)      Log On


   

Question 941182: What does x equal in the problem...
4^(x+1) = (1/2)^(-x)
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
4%5E%28x%2B1%29%22%22=%22%22%281%2F2%29%5E%28-x%29

We want to get both sides to an exponential with the same base.
replace 4 by 2%5E2 and on the right flip the fraction
and change the sign of the exponent to positive.

%282%5E2%29%5E%28x%2B1%29%22%22=%22%222%5Ex

Multiply the exponents on the left

2%5E%282%28x%2B1%29%29%22%22=%22%222%5Ex

Now the base of the exponentials on both sides are the
same positive number (not 1).  So we can equate the
exponents:  

2%28x%2B1%29%22%22=%22%22x

Distribute on the left

2x%2B2%22%22=%22%22x

Add -2 to both sides

2x%22%22=%22%22x-2

Add -x to both sides

x%22%22=%22%22-2

Edwin