Question

If 2^x = y, express the following in terms of y.
$8( {4}^{x - 2} )$

Answer 1

Answer:

answer for the given problem is given

Answer 2

express 4^x in terms of y given that 2^x = y. (B) solve 8(4^x ) – 9(2^x ) + 1 = 0

(A) express 4x in terms of y given that 2x = y. we know that 22 = 4. so 4x = 22^x = (2x )2= y2 .so whenever you have 2C^D it doesnt matter which order you solve. you can do (2C)D or (2D)C (B) solve 8(4x) – 9(2x) + 1 = 0 we can know that; 4x = y2 and 2x = y so, 8(4x) – 9(2x) + 1 = 8(y2) - 9y +1 = 0 what we have left is a quadratic equation to solve (Ay + B)(Cy + D). we know that B and D must either be, both +1 or both -1. 8 can be formed by 4x2 or 8x1 so we know either A or C are 4 and 2 or 8 and 1. Ay X D = 8y X 1 = 8y. Cy X B = y X 1 = y. 8y + y = 9y because it is -9y we know that B and D must be -1. Therefore the quadratic is = (8y - 1)(y - 1) = 0. but we are not finished yet. we have to solve the quadratic. 8y - 1 = 0. 8y = 1 (divide by 8) y = 1/8. 2x = 1/8 a negetive power flips the fraction and we know that 23 is 8. therefore x = -3 second part of quadratic; (y - 1) = 0. y = 1. 2x =1 x = 0

answer is x=0