Question

Pls help me with this question

Answer 1

`\huge{ \boxed{ \bold{ \tt{x = 1}}}}`

Option C is correct.

Explanation:

`\text{First ,\: let's \: know \: about \: exponential \: equation} :`

Exponential Equation

An equation in which variables appears as an exponent of a base is known as exponential equation. The following axioms are useful while solving the exponential equations :

• If
  `\sf{ {a}^(x) = {a}^(b) }` , then x = b
• If aˣ = 1 , then aˣ = a⁰ and x = 0

Thus , while solving an exponential equation, we should simplify the equation till the equation is obtained in the form
`\sf{ {a}^(x) = {a}^(b)}` or aˣ = 1 .

Now, let's start to solve :

`\sf{ {2}^((9x - 3)) = {8}^(( 3 - x))}`

➸
`\sf{ {2}^(9x - 3) = {2}^(3(3 - x)) }`

➸
`\sf{ {2}^(9x - 3) = {2}^(9 - 3x)}`

➸
`\sf{ \cancel{2} ^( \: 9x - 3) = \cancel{2} ^( \: 9 - 3x) }`

➸
`\sf{9x - 3 = 9 - 3x}`

➸
`\sf{9x + 3x = 9 + 3}`

➸
`\sf{12x = 12}`

➸
`\sf{ (12x)/(12) = (12)/(12)}`

➸
`\boxed{ \sf{x = 1}}`

The value of x is 1 .

Hope I helped!

Best regards! :D

~
`\text{TheAnimeGirl}`

Answer 2

option C, x=1

Explanation:

`2^(9x-3) = 8^(3-x)`

`2^(9x-3) = (2^3)^(3-x)`

`2^(9x-3) = 2^(9-3x)`

cut 2 from LHS and RHS you will get,

9x-3 = 9-3x

9x + 3x = 9 + 3

12x = 12

x = 12/12

x = 1

therefore, option C is the correct option

hope it helps you!