9. \( 3-5 \cdot \log _{3} x=2 \)

To solve the equation \( 3-5 \cdot \log _{3} x=2 \), start by isolating the logarithmic term. Subtract 3 from both sides to get \( -5 \cdot \log_{3} x = -1 \). Dividing both sides by -5 gives \( \log_{3} x = \frac{1}{5} \). Now, we can rewrite this in exponential form: \( x = 3^{\frac{1}{5}} \). Thus, the solution is \( x = \sqrt[5]{3} \). Now, how about trying to visualize logarithms? Imagine a world where every number is a cozy little house, and logarithms are the nifty GPS guides helping you find the location of your number in a vast neighborhood called the "number line." They might seem daunting initially, but they transform exponential growth into a more manageable form, making them essential in fields ranging from science to finance! For further exploration, investigating the properties of logarithms can be a treasure trove of insight! Check out how they relate to exponential functions, the change of base formula, or even graphing logarithmic functions. Books like "Understanding Analysis" by Stephen Abbott or "The Joy of x" by Steven Strogatz can offer an engaging approach to these topics, laying a solid foundation in both theory and real-life applications. Happy learning!