Given that w=/x/ and x= 2^b - (8^30+8^5), which of the following values for b yields the lowest value for w?
A)30
B)90
C)91
D)95
E)105
A)30
B)90
C)91
D)95
E)105
For w to be minimum, x must be as close to ZERO as possible.Given that w=/x/ and x= 2^b - (8^30+8^5), which of the following values for b yields the lowest value for w?
A)30
B)90
C)91
D)95
E)105
For x to be Zero, 2^b = (8^30+8^5)
i.e. 2^b = 2^90+2^15
i.e. 2^b = 2^15(2^75+1)
but
2^75+1 = 2^75 (approx.)
therefore 2^b = (2^15)x(2^75+1) = (2^15) x (2^75) = 2^90
therefore, b=90
Answer: Option [spoiler]B[/spoiler]
