Let's convert these exponential equations into logarithmic form.

(a) $e^x = 9$

The logarithmic form of the equation $e^x = 9$ is:

$x = \ln(9)$

This is because logarithms express the exponent to which the base $e$ must be raised to produce 9.

(b) $e^7 = y$

The logarithmic form of the equation $e^7 = y$ is:

$7 = \ln(y)$

This expresses the idea that $7$ is the exponent to which $e$ must be raised to produce $y$.

Would you like more details on how logarithmic conversion works, or have any questions about these?

Here are 5 related questions to deepen your understanding:

1. How would you express $a^x = b$ in logarithmic form for any base $a$?
2. What is the relationship between natural logarithms and the constant $e$?
3. Can logarithmic functions handle negative numbers?
4. How would you solve $\ln(x) = 3$ for $x$?
5. How can you differentiate $\ln(x)$ in calculus?

Tip: Remember that natural logarithms use base $e$, where $e \approx 2.718$.