Question 11 Solve. \( \log _{3}(n)=6 \) \( n=\square \)

Did you know that logarithms originally emerged from the need to simplify complex calculations, especially in astronomy and navigation? The equation \( \log_{3}(n)=6 \) indicates that \( n \) is the result of raising the base, 3, to the power of 6. So, when you solve it, you'll find that \( n = 3^6 = 729 \). To tackle common mistakes when working with logarithms, remember that the base is crucial! Always ensure you recognize your base and apply the exponent correctly. For instance, \( \log_{3}(27) \) is not 9, even though 27 is a neat number; it's actually 3, since \( 3^3 = 27 \). Keep those bases in check to avoid getting lost in the logarithmic wilderness!