if 2^x = y, express the following in terms of y.

Question

a) 2^x+3

b) 2^2x-1

c) 3(2^2-x)

d) 4(2³)^1-x

Answer 1

2^x = y

log₂y= x

2^x+3 = (2^x)(2^3) = 8y

2^2x-1 = (2^2x)/2 = (2^x)(2^x)/2 = (y^2)/2 = .5y^2

3(2^2-x)= 3(2^2)/(2^x) = 3(4)/y = 12/y

4(2^3)^(1-x) = 4(2^(3-3x)) = 4(2^3)/(2^3x)

= 4(8)/(2^x)(2^x)(2^x) = 32/y^3