Question 366565: If x=2 to the power y write 2 to the power 2y and 2 to the 2y+1 in terms of x and
solve the equation 2 to the 2y+1 -5(2 to the y)+2=0 Found 2 solutions by amoresroy, CharlesG2:Answer by amoresroy(361) (Show Source):
You can put this solution on YOUR website! If x=2 to the power y write 2 to the power 2y and 2 to the 2y+1 in terms of x and
x = 2^y
x^2 = 2^2y
2x^2 = 2^(2y+1)
solve the equation 2 to the 2y+1 -5(2 to the y)+2=0
Express above euation in terms of x
2x^2 -5x +2 = 0
Solve for x by factoring method
(2x-1)(x-2) = 0
When 2x-1 = 0
2x = 1
x =1/2
substitute x = 1/2 in equation x = 2^y
2^y = 1/2
Get log of both sides
log 2^y = log 1/2
y log 2 = log 1/2
y = [log 1/2]/log 2
When x-2 = 0
x = 2
substitute x = 2 in equation x = 2^y
2^y = 2
Get log of both sides
log 2^y = log 2
y log 2 = log 2
y = 1
You can put this solution on YOUR website! If x=2 to the power y write 2 to the power 2y and 2 to the 2y+1 in terms of x and solve the equation 2 to the 2y+1 -5(2 to the y)+2=0
x = 2^y
2^(2y) is what in terms of x
2^(2y + 1) is what in terms of x
solve 2^(2y + 1) - 5(2^y) + 2 = 0
logarithmic rule: if b^y = x then logb x = y
in this case b = 2
(