Question 1 (1 point) Identify the common base that should be used to solve the equation below. \[ \begin{array}{l}2^{x-4}=8^{3 x+5} \\ 16 \\ 2\end{array} \] \[ \begin{array}{l}4\end{array} \]

To solve the equation \(2^{x-4} = 8^{3x+5}\), it's key to recognize that both sides can be rewritten using the same base. Notably, \(8\) can be expressed as \(2^3\), which means \(8^{3x+5}\) can be rewritten as \((2^3)^{3x+5} = 2^{(3)(3x+5)} = 2^{9x+15}\). Thus, all terms can be framed in terms of the base \(2\). Using the same base makes it easier to equate the exponents, leading to a simple algebraic equation. Just remember that simplifying bases can be a marvelous shortcut in the foreboding world of exponents! When you work with exponential equations, it’s essential to ensure that both sides are expressed in the same base before attempting to solve. A common mistake is to rush into calculations without verifying that the bases align. This can lead to incorrect solutions and confusion, so always check your bases first before diving into the math!