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Find The Value Of x ?
[tex]1) \sf \large \: log_{3}( \frac{1}{3} ) = x[/tex]

[tex]2) \large\sf log_{3}(x - 1) = 2[/tex]
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Respuesta :

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Answer:

1) [tex]x = -1[/tex]  ||     2) [tex]x = 10[/tex]

Explanation:

1)

→ [tex]\log _3\left(\frac{1}{3}\right)=x[/tex]

→ [tex]\frac{1}{3} = 3^x[/tex]

→ [tex]3^{-1} = 3^x[/tex]

→ [tex]x = -1[/tex]

2)

→ [tex]\log _3\left(x-1\right)=2[/tex]

→ [tex]x - 1 = 3^2[/tex]

→ [tex]x -1 = 9[/tex]

→ [tex]x = 9 +1[/tex]

→ [tex]x = 10[/tex]

DᴀʀᴋPᴀʀᴀᴅᴏx

[tex]\qquad \qquad\huge \underline{\boxed{\sf Answer}}[/tex]

Here's the solution ~

Question 1 :

[tex]\qquad \sf  \dashrightarrow \: log_{ {3} }( \frac{1}{3} ) = x[/tex]

[tex]\qquad \sf  \dashrightarrow \: log_{ {3} }( {3}^{ - 1} ) = x[/tex]

[tex]\qquad \sf  \dashrightarrow \: log_{ {3} }( {3})^{ - 1 } = x[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 1 \times log_{3}(3) = x[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 1 \times 1 = x[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = - 1[/tex]

Question 2 :

[tex]\qquad \sf  \dashrightarrow \: log_{3}(x - 1) = 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: x - 1 = {3}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 9 + 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 10[/tex]