Discussion

Question:

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

Explanation:

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

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