Find the values of a and b such that the graph of y = log2(x+b) goes through the points of (8,10) and (32,14)

Question

Find the values of a and b such that the graph of y = log2(x+b) goes through the points of (8,10) and (32,14)

Answer 1

through (8,10) and (32,14)

y = alog(x+b) with log to the base 2

10= alog₂(8+b)

log10 = a(8+b) = ln10/ln2

ab = ln10/ln2 - 8a=12.678-8a

b = 12.678/a - 8

14 = log(24 -12.678/a)

log14 = ln14/ln2 = 24-12.678/a

12.678/a = 24-ln14/ln2

a = 12.678/(24-ln14/ln2) = 0.6279

b = 12.678/a - 8= (12.678/12.678/(24-ln14/ln2) -8

= 24-ln14/ln2 -8

=20.1926

f(x) = .6279log₂(x+20.1926)