To calculate $\log_9 14$ using the change of base formula, we use the following equation:

$\log_b a = \frac{\log_c a}{\log_c b}$

Here, $c$ is any base we choose. Common choices are base 10 (common logarithm) or base $e$ (natural logarithm). Let’s proceed using base 10:

$\log_9 14 = \frac{\log_{10} 14}{\log_{10} 9}$

Now compute each logarithm:

1. $\log_{10} 14 \approx 1.1461$
2. $\log_{10} 9 \approx 0.9542$

Substitute these values into the formula:

$\log_9 14 = \frac{1.1461}{0.9542} \approx 1.2016$

Final Answer:

$\log_9 14 \approx 1.2016$

Would you like further details on logarithms or their properties?

---

Related Questions:

1. How is the change of base formula derived?
2. Can the natural logarithm (base $e$) be used instead of base 10?
3. What are some practical applications of logarithms?
4. How does changing the base affect the calculation?
5. How can logarithms be used to solve exponential equations?

Tip:

Always double-check your calculations when using a calculator for logarithmic values, as small errors can propagate in larger computations!