Questions: Write in logarithmic form. 1/9=3^(-2) The logarithmic form is □ (Use integers or fractions for any numbers in the expression.)

$Write in logarithmic form. 1/9=3^(-2) The logarithmic form is □ (Use integers or fractions for any numbers in the expression.)$

Transcript text: Write in logarithmic form. \[ \frac{1}{9}=3^{-2} \] The logarithmic form is $\square$ (Use integers or fractions for any numbers in the expression.)

Solution

Solution Steps

To convert the given exponential equation $\frac{1}{9} = 3^{-2}$ into logarithmic form, we need to express it in the form $\log_{\text{base}}(\text{result}) = \text{exponent}$. Here, the base is 3, the result is $\frac{1}{9}$, and the exponent is $-2$.

Step 1: Convert to Logarithmic Form

We start with the equation: \[ \frac{1}{9} = 3^{-2} \] To express this in logarithmic form, we rewrite it as: \[ \log_{3}\left(\frac{1}{9}\right) = -2 \]

Step 2: Simplify the Result

The fraction $\frac{1}{9}$ can be expressed as $3^{-2}$, confirming that: \[ \log_{3}\left(3^{-2}\right) = -2 \] This shows that our logarithmic form is consistent with the original equation.