d. \( 2 \cdot 3^{x}-18=0 \)

To solve the equation \( 2 \cdot 3^{x}-18=0 \), we first isolate the term involving \( x \). Adding 18 to both sides gives us \( 2 \cdot 3^{x} = 18 \). Next, we divide both sides by 2, resulting in \( 3^{x} = 9 \). Since \( 9 \) can be rewritten as \( 3^2 \), we set \( 3^{x} = 3^{2} \). Therefore, we can equate the exponents to find \( x \): \( x = 2 \). Now, let’s take a fun peek into the world of exponents: Did you know that ancient civilizations, such as the Babylonians, used rudimentary forms of exponentiation in their mathematical practices? Their innovative ways of solving problems paved the way for what we now recognize as algebra! For some practical applications, exponential equations like this one arise in fields such as finance (when calculating compound interest) and science (like population growth models). Understanding exponentials can help make sense of trends and patterns in various real-life scenarios!