algebra question

-1.5 = x 

 

If you approach the problem as .25^(x)=16 it simplifies the equation quite a bit. Using exponents we know that raising a fraction to a negative number allows us to "flip" the fraction upside down giving us the new equation 4^(x) = 16 from there we can logically see that 4^(2) = 16. This brings us to the second part of the equation (2x+1) = -2 remember that the 2 needs to be negative in order for us to flip our fraction. Applying simple algebra we arrive at our final answer that -1.5 = x

Solve for x over the real numbers:
4^(-1-2 x) = 16

Take reciporicals of both sides:
4^(2 x+1) = 1/16

Take the logarithm base 4 of both sides:
2 x+1 = -2

Subtract 1 from both sides:
2 x = -3

Divide both sides by 2:
Answer: |x = -3/2