f(x)=log(5x)
We want the curve to pass through (5,-2)
We can move the curve along the plot adding something in the formula. Let’s call that z.
You can put z in different parts of the formula and still find a z value that makes it pass through the point (5,-2). I will choose to put it inside the log:
f(x)=log(5x+z)
f(5)=-2
log(5*5+z)=-2
log(25+z)=-2
10^-2 = 25+z
10^-2 – 25 = z
z=1/100-25 = 1/100-2500/100=-2499/100 = -24.99
Let’s verify:
f(5)= log(5*5-24.99)=-2
So the formula: f(x)=log(5x-24.99) passes through the point (5,-2)