Question

12) Find the value of a
a, If log³(1/243)=-9
,​

Answer 1

Answer in the photo

pls mark IT As Branliest

Answer 2

${ \large{ \sf{ \underbrace{\underline{\bigstar \:Answer:}}}}}$

The value of a is 5

${ \large{ \sf{ \underbrace{\underline{\bigstar \:Explanation:}}}}}$

To answer this question, we need to highlight the law of logarithm that is in line with the given question.

${ \large{ \sf{ \underbrace{\underline{\bigstar Given:}}}}}$

$\sf{㏒ₓ a = n}$

$\sf{Then xⁿ = a}$

Rewriting the question we have:

$\sf{㏒₃ 243⁻¹ = - a}$

Lets write 243 in power form. we have:

$\sf{243 = 3⁵}$

$\sf{So, ㏒₃3⁻⁵ = - a}$

From the logarithmic law given above, we have that:

$\sf{3^{-a}3 −a = 3⁻⁵}$

Since they have the same base:

$\sf{-a = -5}$

$\sf{a = 5}$

${ \large{ \boxed{ \red{ \underline{ \bf \:The\: value\: of \:a\: =\:5}}}}}$

Learn more:-

$\begin{gathered}\boxed{\begin{array}{c}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end {array}}\end{gathered}$