Question

Let $p=\sqrt[3]{11+2\sqrt{30}}+\sqrt[3]{11-2\sqrt{30}}$, then the value of ${\log }_5\left(p^3-3p+3\right)$ is equal to

• A. -2
• B. 0
• C. 1
• D. 2

Answer 1

Answer: (D)

$p^3=11+2\sqrt{30}+11-2\sqrt{30}+3[(11+2\sqrt{30})(11-2\sqrt{30}){]}^{1/3}(P)$
$\Rightarrow p^3=22+3p\Rightarrow p^3-3p+3=25$
$\Rightarrow {\log }_5(25)=2$