Question

If $\log _a 4-\log _4 a=7$ then the value of $\left(\log _a 4\right)^2+\left(\log _4 a\right)^2$ is equal to $(0

• A. 51
• B. 47
• C. 53
• D. 45

Answer 1

Answer: (A)

Given $\log _{ a } 4-\log _4 a =7 \Rightarrow\left(\log _{ a } 4\right)^2+\left(\log _4 a \right)^2-2=49$ (squaring both sides)
$\therefore\left(\log _a 4\right)^2+\left(\log _4 a\right)^2=51$.