Question

If $x={\log }_{2\sqrt{3}}1728$, then the value of x is

• A. 5
• B. 6
• C. 7
• D. 8

Answer 1

The correct option is B 6

Given that $x={\log }_{2\sqrt{3}}1728\Rightarrow {\left(2\sqrt{3}\right)}^x=1728\Rightarrow 2^x\cdot {\left(\sqrt{3}\right)}^x=2^6\cdot 3^3\Rightarrow 2^x\cdot 3^{\frac{x}{2}}=2^6\cdot 3^3\mathrm{Comparing}\mathrm{both}\mathrm{sides},\mathrm{we}\mathrm{get}x=6$