Question

Express the following in logarithmic form$:$
$81=3^4$

• A. ${\log }_{3}81=4$
• B. ${\log }_{9}81=2$
• C. $2{\log }_{3}9=4$
• D. $4{\log }_{9}3=2$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A ${\log }_{3}81=4$
B ${\log }_{9}81=2$
C $2{\log }_{3}9=4$
D $4{\log }_{9}3=2$

$y=a^x\Rightarrow {\log }_{a}y=x\therefore 81=3^4\Rightarrow {\log }_{3}81=4$

A is true.

$81=3^4=9^2$

$\Rightarrow {\log }_{9}81={\log }_9{9}^2=2{\log }_{9}9=2$

B is true.

$81=3^4=9^2$

$\Rightarrow {\log }_3{3}^4={\log }_3{9}^2=2{\log }_{3}9$

C is true.

$81=3^4=9^2$

$\Rightarrow {\log }_9{3}^4={\log }_9{9}^2=2{\log }_{9}9=2$

$\Rightarrow 4{\log }_{9}3=2$

D is true.