The log function can be graphed using the vertical asymptote at x = 1 and the points (2,0), (5,1) & (3,0.5).
Given graph is 
We have to find the asymptotes.
Set the argument of the logarithm equal to zero.
x - 1 = 0
Now add 1 to both the sides of the equation.
x - 1 + 1 = 0 + 1
= x = 1
The vertical asymptote occurs at x = 1
So, vertical asymptote: x = 1
Now, find the point at x = 2
Replace the variable x with 2 in the expression.

Simplify the result
Subtract 1 from 2

Logarithm base 4 of 1 is 0
f(2) = 0
The final answer is 0.
y = 0
Now find the point at x = 5
Replace the variable x with 5 in the expression.


Logarithm base 4 of 4 is 1
so, f(5) = 1
y = 1
Now find the point at x = 3
Replace the variable x with 3 in the expression.


Logarithm base 4 of 2 is
.
Rewrite as an equation.

Rewrite
in exponential form using definition of a logarithm. If x and b are positive real numbers and b does not equal 1, then
is equivalent to 

Create expressions in the equation that all have equal bases.

Rewrite 

Since the bases are the same, then two expressions are only equal if the exponents are also equal.
2x = 1
solve for x

The variable x is equal to 

The final answer is 
So, y = 0.5
The log function can be graphed using the vertical asymptote at x = 1 and the points (2,0), (5,1) & (3,0.5).
x y
2 0
3 0.5
5 1
Hence the answer is the log function can be graphed using the vertical asymptote at x = 1 and the points (2,0), (5,1) & (3,0.5).
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