Question

If ${\log }_{9}243=x$, then the value of $x$ is equal to

• A. $\frac{3}{2}$
• B. $\frac{5}{2}$
• C. $\frac{2}{5}$
• D. $\frac{2}{3}$

Answer 1

The correct option is B $\frac{5}{2}$

${\log }_{9}243=\frac{\log 243}{\log 9}$ ...$({\log }_{b}a=\frac{\log a}{\log b})$

$\therefore \frac{\log 243}{\log 9}=x$

$\therefore x=\frac{\log 3^5}{\log 3^2}$

$\therefore x=\frac{5}{2}$ ...($\log a^b=b\log a$)