Question

If ${\log }_2[{\log }_3\{lo{g}_4({\log }_{5}x)\}]=0,$ then the value of x is

• A. $5^{24}$
• B. $1$
• C. $2^{25}$
• D. $5^{64}$

Answer 1

Answer: (D)

Given that, ${\log }_2[{\log }_3\{{\log }_4({\log }_{5}x)\}]=0$
$\Rightarrow$ ${\log }_3\{{\log }_4({\log }_{5}x)\}=2^0=1$
$\Rightarrow$ ${\log }_4({\log }_{5}x)=3^1=a$
$\Rightarrow$ ${\log }_{5}x=4^3=64$
$\Rightarrow$ $x=5^{64}$