Math problem

Question

Find the equation of the logarithmic function passing through the points (1,0) and (3,1/2).

Answer 1

The general form is:

y = A*logx + B

 

since we know the x and y values at 2 points, we can write 2 equations for A an B

 

for x=1, y=0:

0 = A*log1 + B

 

for x=3, y=0.5:

0.5 = Alog3 + B

 

from the 1st equation, log1 = 0, therefore B = 0

 

then, the 2nd equation is:

0.5 = Alog3

A = 0.5 /log3 = 0.455

 

so, the equation is:

y = 0.455*logx

Answer 2

Consider the parent function y=ln(x).  It passes through (1,0) because ln(1)=0.

 

However, ln(3) is not 1/2.

 

Suppose y=A*ln(x).  It is still true that the curve passes through (1,0), so this form is a possibility.

 

Now, we want 1/2 = A*ln(3).

 

So, A=(1/2)/ln(3)  works.