Question

Find the distance between the points (log9 base 3 ,log1 base 3) and (0,3)

Answer 1

Answer:

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Answer 2

The distance between the points (log₃ 9 ,log₃ 1 ) and (0,3) = √13 units

Given:

Points (log₃ 9 ,log₃ 1 ) and (0,3)

To find:

The distance between (log₃ 9 ,log₃ 1 ) and (0,3)

Solution:

Given points  (log₃ 9 ,log₃ 1 ) and (0,3)  

For simple calculation change the point as shown below

㏒₃ 9 = ㏒₃ 3² = 2 ㏒₃ 3 = 2 (1) = 2             [ ∵  ㏒ₐ a = 1 ]  

log₃ 1 = 0

From above calculation

(log₃ 9, log₃ 1) = (2, 0)

Now find distance between (2, 0) and (0, 3)

As we know the formula for distance between two points

(x₁, y₁) and (x₂, y₂) is given by

                  √(x₂-x₁)² + (y₂- y₁)²  

Take (x₁, y₁) = (2, 0) and (x₂, y₂) = (0, 3)  

distance =  √(0 - 2)² + (3 - 0)² = √(2)² + (3)² = √4 + 9 = √13  

Therefore,

The distance between the points (log₃ 9 ,log₃ 1 ) and (0,3) = √13 units

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