Question: Solve the following logarithmic equation: \[ \log_3(3^{-4}) = x \] Enter your answer (opens in…

Solve the following logarithmic equation:

\[ \log_3(3^{-4}) = x \]

Enter your answer (opens in new window)

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

Solution

To solve the logarithmic equation: \[ \log_3 (3^{-4}) = x \] First, recognize that the logarithmic expression \(\log_b (b^a)\) is equal to \(a\). So, for the given equation: \[ \log_3 (3^{-4}) = -4 \] Thus, \[ x = -4 \] So, the value of \(x\) is \(-4\).