Express the logarithm ln(9)=2.19722 (to 5 decimal places) in its exponential form

1. Break Down the Problem

To express the logarithmic equation $\ln(9) = 2.19722$ in exponential form, we need to understand the relationship between logarithms and exponents. The general form is: $\ln(a) = b \implies a = e^b$ where $e$ is the base of natural logarithms (approximately 2.71828).

2. Relevant Concepts

Here, we can use the property of logarithms that states: $\ln(a) = b \implies a = e^b$

3. Analysis and Detail

In our case, setting $a = 9$ and $b = 2.19722$, we can rewrite the equation in exponential form.

4. Verify and Summarize

By applying the formula: $9 = e^{2.19722}$ This shows that the exponential form of $\ln(9) = 2.19722$ is indeed $9 = e^{2.19722}$.

Final Answer

Thus, the exponential form of $\ln(9) = 2.19722$ is: $9 = e^{2.19722}$