Question

Find the value of a, if log(1/243) base 3
=
-a.​

Answer 1

$\huge\mathtt{Hello!}$

$log_{3}( \frac{1}{243} ) = - a$

$log_{3}( {243}^{ - 1} )$

$= - log_{3}( {3}^{5} )$

$= - 5 log_{3}(3)$

$= - 5 \times 1$

$- a = - 5$

$a = 5$

Therefore, value of a is five

@prettynightmare

Answer 2

The value of a is 5.

Step-by-step explanation:

We have,

$\log_3(\dfrac{1}{243})=-a$

To find, the value of a = ?

∴ $\log_3(\dfrac{1}{243})=-a$

Using the logarithm identity,

$\log \dfrac{m}{n} =\log m-\log n$

⇒ $\log_31-\log_3243=-a$

⇒ 0 - $\log_33^5$ = - a [∵ $\log 1$ = 0]

⇒ - 5$\log_33$= - a

Using the logarithm identity,

$\log a^m=m\log a$

⇒ - 5(1) = - a

Using the logarithm identity,

$\log_aa$ = 1

⇒ - 5 = - a

⇒ a = 5

Thus, the value of a is 5.