Question: Solve the following logarithmic equation in terms of the variable \( x \): \[ \log_4(x) = -2…

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

\[ \log_4(x) = -2 \]

Answer

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\[ x = \boxed{\phantom{0}} \]

Solution

To solve the logarithmic equation \(\log_4(x) = -2\) in terms of the variable \(x\), we can rewrite the equation in its exponential form. Start by converting the logarithmic equation to an exponential equation: \[ 4^{-2} = x \] Calculate \(4^{-2}\): \[ x = \frac{1}{4^2} \] Simplify the expression: \[ x = \frac{1}{16} \] Thus, the solution is: \[ x = \frac{1}{16} \]