Question

${\log }_3\left(\frac{{\log }_3{3}^{3^{3^3}}}{{\log }_{3^3}{3}^{3^3}}\right)$ has the value equal to

• A. 9
• B. 25
• C. 27
• D. 18

Answer 1

Answer: (B)

${\log }_3\left(\frac{3^{3^3}}{3^2}\right)={\log }_3\left(\frac{3^{27}}{3^2}\right)\left[{\log }_{3^3}{3}^{3^3}=\frac{{\log }_3{3}^{3^3}}{{\log }_3{3}^3}=\frac{3^3}{3}=3^2\right]$
$={\log }_3\left(3^{25}\right)=25$