Question

If A(log₂ 8, log₅ 25) and B(log₁₀ 10, log₁₀ 100), then the mid-point of AB is 

A) (2, 2) 

B) (3, 2) 

C) (1, 2) 

D) (4, 4)

Answer 1

Correct option is (A) (2, 2)

\(\because\) \(log_2\,8=log_2\,2^3\)

\(=3\,log_2\,2=3\)         \((\because log_a\,a=1)\)

\(log_5\,25=log_5\,5^2\)

\(=2\,log_5\,5=2\)

\(log_{10}\,10=1\)

and \(log_{10}\,100=log_{10}\,10^2\)

\(=2\,log_{10}\,10=2\)

\(\therefore\) \(A=(log_2\,8,log_5\,25)=(3,2)\)

& \(B=(log_{10}\,10,log_{10}\,100)=(1,2)\)

\(\therefore\) Mid-point of AB is mid-point of (3, 2) & (1, 2)

\(=(\frac{3+1}2,\frac{2+2}2)\)

\(=(\frac{4}2,\frac{4}2)=(2,2)\)

Answer 2

Correct option is A) (2, 2)