Which of the following points does not lie on the graph of y = log₃x?
(0, 1), (27, 3), (1, 0)

Solution:

Given, the logarithmic equation is y = log₃x

We have to check which point does not lie on the graph of the given equation.

Substitute the value of x-coordinates in the equation and find the corresponding y coordinate.

From the option,

A) (0, 1)

The x-coordinate is 0.

y = log₃(0)

The value of log 0 is undefined.

Therefore, the point (0, 1) does not lie on the graph.

B) (27, 3)

The x-coordinate is 27

y = log₃(27)

y = log₃3₃

By using logarithmic property,

\(log_{b}a^{m}=mlog_{b}a\)

So, y = 3log₃3

y = 3

Therefore, the point (27, 3) lies on the graph.

C) (1, 0)

The x-coordinate is 1

y = log₃1

y = 0

Therefore, the point (1, 0) lies on the graph.

Therefore, point (1, 0) does not lie on the graph.

---

Which of the following points does not lie on the graph of y = log₃x?

Summary:

The point (1, 0) does not lie on the graph of y = log₃x.