The equation for the transformed logarithm shown in the diagram, which passes through the points (2, 0), and (1, 2) is; f(x) = 2·log₂(3 - x)
The equation is found as follows;
Let the form of the equation be y = a·log(b - x)
The point (2, 0), indicates that we get;
0 = a·log(b - 2)
log(b - 2) = 0/a
log(b - 2) = 0
x⁰ = b - 2
1 = b - 2
b = 1 + 2
b = 3
The point (1, 2), indicates that we get;
2 = a·log(3 - 1)
a = 2/(log(3 - 1))
a = 2/(log(2))
The equation is therefore; y = (2/(log(2)))·log(3 - x)
(2/(log(2)))·log(3 - x) = 2·log₂(3 - x)
Therefore, the equation is; f(x) = 2·log₂(3 - x)