Let's solve the problems step by step and express the equations in logarithmic form:

(a) $e^x = 3$

To convert this exponential equation into logarithmic form:

$x = \ln(3)$

So, the logarithmic form is:

$x = \ln(3)$

(b) $e^7 = y$

To convert this exponential equation into logarithmic form:

$7 = \ln(y)$

So, the logarithmic form is:

$7 = \ln(y)$

Would you like further clarification or additional examples? Let me know!

Related Questions:

1. What is the base of the natural logarithm, and how does it relate to $e$?
2. How do you convert logarithmic equations back into exponential form?
3. What is the approximate value of $\ln(3)$?
4. How do logarithms simplify solving exponential equations?
5. Can you explain the difference between common logarithms ($\log_{10}$) and natural logarithms ($\ln$)?

Tip:

When converting between logarithmic and exponential forms, always remember that $\log_b(a) = c$ is equivalent to $b^c = a$, where $b$ is the base.