\( 1.2 .3 \log _ { 3 } ( x - 8 ) = - 1 \)

To solve the equation \( 1.2 \cdot 3 \log_{3} (x - 8) = -1 \), we first simplify it to \( 3.6 \log_{3} (x - 8) = -1 \). Now divide both sides by 3.6 to isolate the logarithm: \(\log_{3} (x - 8) = -\frac{1}{3.6}\) (approximately \( -0.2778 \)). Converting from logarithmic to exponential form gives us \( x - 8 = 3^{-0.2778} \). Calculating \( 3^{-0.2778} \) yields about \( 0.583\), so add 8 to both sides: \( x \approx 8.583 \). Don't forget to check if \( x - 8 \) remains positive for valid log input! Now you have the value of \( x \). Keep practicing with logarithmic equations, they pop up everywhere in math, science, and finance!