algebra puzzle

battery123
Posers and Puzzles 07 Nov '07 17:41
1. 07 Nov '07 17:41
2^(2Y+1)+7(2^Y)-15=0
find y to 2 d.p. and show your working
2. PBE6
Bananarama
07 Nov '07 18:221 edit
Originally posted by battery123
2^(2Y+1)+7(2^Y)-15=0
find y to 2 d.p. and show your working

2^(2y+1) + 7(2^y) - 15 = 0

(2^2y)(2^1) + 7(2^y) - 15 = 0

2(2^y)^2 + 7(2^y) - 15 = 0

Now let 2^y = x and we end up with something quite familiar:

2x^2 + 7x - 15 = 0

Solving this using the quadratic formula, we get:

x = (-7 +/- 13)/4

Therefore:

x = 3/2 or x = -5

However, since x = 2^y, and the exponential function is always positive, we must reject the negative solution. Therefore:

x = 3/2 = 2^y

Taking the log base 2 ("log2" ) of both sides we have:

y = log2(3/2) = log2(3) - log2(2) = log2(3) - 1

Evaluating this expression numerically to 2 decimal places we get:

y = 0.58
3. 07 Nov '07 19:57
Originally posted by PBE6
Evaluating this expression numerically to 2 decimal places we get:

y = 0.58
Looks sound to me.