Question

Let $S={\log }_2(\sqrt{7}+\sqrt{5})$, then the value of ${\log }_2(\sqrt{7}-\sqrt{5})$ in terms of $S$, is

• A. $\frac{2}{S}$
• B. $\frac{S-1}{S}$
• C. $1-S$
• D. $2-S$

Answer 1

Answer: (C)

${\log }_2(\sqrt{7}-\sqrt{5})={\log }_2\left(\frac{2}{\sqrt{7}+\sqrt{5}}\right)={\log }_{2}2-{\log }_2(\sqrt{7}+\sqrt{5})=1-S$