Question

Find the mid point of AB, where
A( log, 8, log2 25) and
B(log10 10, log10 100).
100).
​

Answer 1

SOLUTION

TO DETERMINE

The mid point of AB, where

$\sf{A ( log_{2}8, log_{5}25 ) \: \: B( log_{10}10, log_{10}100 )}$

FORMULA TO BE IMPLEMENTED

For the given two points

$\sf{A( x_1 , y_1) \: \: and \: \: B( x_2 , y_2)}$

The midpoint of the line AB is

$\displaystyle \sf{ \bigg( \frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} \bigg)}$

EVALUATION

Here the given points are

$\sf{A ( log_{2}8, log_{5}25 ) \: \: B( log_{10}10, log_{10}100 )}$

Now

$\sf{ log_{2}(8) = log_{2}( {2}^{3} ) = 3 \: log_{2}(2) = 3 }$

$\sf{ log_{5}(25) = log_{5}( {5}^{2} ) = 2 \: log_{5}(5) = 2 }$

$\sf{ log_{10}(10) = 1 }$

$\sf{ log_{10}(100) = log_{10}( {10}^{2} ) = 2 \: log_{10}(10) = 2 }$

So the points are simplified to

A (3,2) , B (1,2)

Hence the required midpoint is

$\displaystyle \sf{ = \bigg( \frac{3 + 1}{2} , \frac{2 + 2}{2} \bigg)}$

$\displaystyle \sf{ = \bigg( \frac{4}{2} , \frac{4}{2} \bigg)}$

$\displaystyle \sf{ = (2 , 2)}$

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Answer 2

Answer:

answer is (2,2)

hope it helps you.

thankyou.