Question

The value of ${\log }_{2\sqrt{3}}1728$ is equal to

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

Answer: (D)

$6$

Let ${\log }_{2\sqrt{3}}1728=x$

$⟹1728=\left(2\sqrt{3}\right){}^x⟹(1728=2^6\times 3^3=2^6{\sqrt{3}}^6)\therefore 2^6{\left(\sqrt{3}\right)}^6={\left(2\sqrt{3}\right)}^x\therefore x=6$