XAT 2019 — QA & DI Question 10

LogarithmsEasy

$\frac{\log (97 - 56 \sqrt{3})}{\log (\sqrt{7 + 4 \sqrt{3}})}$ equals which of the following?

Answer & solution

A
-5
B
-3
C
None of the others
-4
E
-2

Solution

Given $\frac{\log (97 - 56 \sqrt{3})}{\log (\sqrt{7 + 4 \sqrt{3}})}$

= $\frac{\log {(7 - 4 \sqrt{3})}^{2}}{\log {(7 + 4 \sqrt{3})}^{1 / 2}}$

Now, $7 + 4 \sqrt{3}$ = $\frac{1}{7 - 4 \sqrt{3}}$

⇒ $\frac{\log {(7 - 4 \sqrt{3})}^{2}}{\log {(7 + 4 \sqrt{3})}^{1 / 2}}$ = $\frac{\log {(7 - 4 \sqrt{3})}^{2}}{\log {(7 - 4 \sqrt{3})}^{- 1 / 2}}$ = $\frac{2}{- 1 / 2}$ = -4

XAT 2019 QA & DI Q10: log 97 - 56 3 log 7 + 4 3 equals which of the following? — Solution | TheCATExam