Question: Solve the following logarithmic equation in terms of the variable \( x \): \[ \log_9(x) =…

Solve the following logarithmic equation in terms of the variable \( x \):

\[ \log_9(x) = \frac{-1}{2} \]

Answer:

\( x = \boxed{\phantom{0}} \)

Solution

To solve the logarithmic equation for \( x \): We start with the equation: \[ \log_9(x) = -\frac{1}{2} \] Rewrite the logarithmic equation in exponential form: \[ x = 9^{-\frac{1}{2}} \] Calculate \( 9^{-\frac{1}{2}} \): \[ x = \frac{1}{\sqrt{9}} \] Since \(\sqrt{9} = 3\), simplify to: \[ x = \frac{1}{3} \] Therefore, the solution is \( x = \frac{1}{3} \).