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 $(0<a\ne 1)$

• 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)
$\therefore {\left({\log }_{a}4\right)}^2+{\left({\log }_{4}a\right)}^2=51$.