Question

❤HEY DEAR❤

GOOD MORNING ✌✌

Solve the following equation :-
$log_{3}( {3}^{x} - 8 ) = 2 - x$
°•○●□■▪☆50 POINTS☆■□●○•°

#QUALITY CONTENT ✔✔
#NO SPAM ❎​

Answer 1

$\huge\mathfrak{hello \: mate!} \\ \\ </p><p></p><p>{your \: answer:}$

this question can be also written as ,by the converting into exponential form we get

⇛3^x-8=3^(2-x)

⇛3^x-8= 9/3^x

let 3^x = y

⇛y-8=9/y

⇛y²-8y-9=0

⇛y²-9y+y-9=0

⇛y(y-9)+1(y-9)=0

⇛y= -1 and 9

but 3^x can't be negative it will be POSTIVE

⇛3^x=9

⇛3^x=3³

⇛x=2

$\huge\mathfrak{be \: Brainly }$

Answer 2

Answer:

x = 2

Step-by-step explanation:

$Given:log_{3}(3^x - 8) = 2 - x$

$\boxed{if \ x = b^y, \ then \ log_{b} \x = y}$

$\Longrightarrow 3^x - 8 = 3^{2 - x}$

$\Longrightarrow 3^x - 3^{2 - x} = 8$

$\Longrightarrow 3^x - 3^{2 - x} = 3^2 - 1$

$\Longrightarrow 3^x - 3^{2 - x} = 3^2 - 3^0$

$\Longrightarrow 3^x - 3^{2 - x} = 3^2 - 3^{2 - 2}$

$\textbf{On \ Comparing \ both \ sides,\ we \ get}$

$\Longrightarrow \textbf {x = 2}$

Hope it helps!