Question

Find The Value Of x ?


`1) \sf \large \: log_(3)( (1)/(3) ) = x`


`2) \large\sf log_(3)(x - 1) = 2`
Thankuhh☃️​

Answer 1

`\qquad \qquad\huge \underline{\boxed{\sf Answer}}`

Here's the solution ~

Question 1 :

`\qquad \sf  \dashrightarrow \: log_{ {3} }( (1)/(3) ) = x`

`\qquad \sf  \dashrightarrow \: log_{ {3} }( {3}^( - 1) ) = x`

`\qquad \sf  \dashrightarrow \: log_{ {3} }( {3})^( - 1 ) = x`

`\qquad \sf  \dashrightarrow \: - 1 * log_(3)(3) = x`

`\qquad \sf  \dashrightarrow \: - 1 * 1 = x`

`\qquad \sf  \dashrightarrow \: x = - 1`

Question 2 :

`\qquad \sf  \dashrightarrow \: log_(3)(x - 1) = 2`

`\qquad \sf  \dashrightarrow \: x - 1 = {3}^(2)`

`\qquad \sf  \dashrightarrow \: x = 9 + 1`

`\qquad \sf  \dashrightarrow \: x = 10`

Answer 2

1)
`x = -1` || 2)
`x = 10`

Step-by-step explanation:

1)

→
`\log _3\left((1)/(3)\right)=x`

→
`(1)/(3) = 3^x`

→
`3^(-1) = 3^x`

→
`x = -1`

2)

→
`\log _3\left(x-1\right)=2`

→
`x - 1 = 3^2`

→
`x -1 = 9`

→
`x = 9 +1`

→
`x = 10`