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If 3^(x)= (1)/(9), then the value of x i...

If `3^(x)= (1)/(9)`, then the value of x is

A

2

B

`-2`

C

`(1)/(2)`

D

1

Text Solution

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The correct Answer is:
To solve the equation \(3^x = \frac{1}{9}\), we can follow these steps: ### Step 1: Rewrite \(\frac{1}{9}\) in terms of base 3 We know that \(9\) can be expressed as \(3^2\). Therefore, we can rewrite \(\frac{1}{9}\) as: \[ \frac{1}{9} = \frac{1}{3^2} = 3^{-2} \] ### Step 2: Set the exponents equal to each other Now that we have \(3^x = 3^{-2}\), we can set the exponents equal to each other since the bases are the same: \[ x = -2 \] ### Conclusion Thus, the value of \(x\) is: \[ \boxed{-2} \]
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