Let's solve the two logarithmic expressions shown in the image:

1. log 10: This is a base-10 logarithm. When no base is specified in a logarithmic expression, the base is assumed to be 10.

   Using the logarithmic rule: $\log_b(b^x) = x$ Since $\log_{10}(10)$, the base and the number are both 10, the result is: $\log 10 = 1$

2. ln $e^3$: The natural logarithm (ln) is the logarithm to the base $e$. Using the property: $\ln(e^x) = x$ Since $e^3$ is the input, the result is: $\ln(e^3) = 3$

Final answers:

1. $\log 10 = 1$
2. $\ln e^3 = 3$

Would you like any more details or explanations?

Here are some related questions:

1. What is the value of $\log 100$?
2. How do you simplify $\ln(e^{2x})$?
3. What is the result of $\log_b(b^x)$ in general form?
4. How do you solve $\log_2(8)$?
5. What is the base of the natural logarithm?

Tip: Remember, the logarithmic and exponential functions are inverses of each other. This makes simplifying expressions involving $\ln$ and $\log$ straightforward when their bases match!