SUMMARY
The expression $a^{5/\log_9a}$ can be converted to base 14 by utilizing the change of base formula for logarithms. Specifically, the conversion involves rewriting the logarithm in the expression using base 14. The key steps include applying the formula $\log_b a = \frac{\log_k a}{\log_k b}$, where $k$ is any base, to facilitate the conversion. This method is essential for accurately transforming logarithmic expressions across different bases.
PREREQUISITES
- Understanding of logarithmic properties and change of base formula
- Familiarity with exponential functions and their transformations
- Basic knowledge of mathematical notation and expressions
- Ability to manipulate algebraic expressions
NEXT STEPS
- Study the change of base formula for logarithms in detail
- Practice converting logarithmic expressions to various bases
- Explore exponential functions and their applications in different bases
- Review advanced algebra techniques for manipulating complex expressions
USEFUL FOR
Students studying algebra, mathematicians working with logarithmic expressions, and educators teaching logarithmic conversions.