Express the logarithm ln(8)=2.07944 (to 5 decimal places) in its exponential form. For example, log525=2 is equivalent to 52=25

Break Down the Problem

1. Identify the given logarithmic expression: $\ln(8) = 2.07944$.
2. Recall the relationship between logarithms and exponentials.

Relevant Concepts

Using the property of logarithms:

• For any logarithm $\log_b(a) = c$, the equivalent exponential form is given by $b^c = a$.
• In this case, we use the natural logarithm base $e$.

Analysis and Detail

1. From $\ln(8) = 2.07944$, we can express this in exponential form.
2. Here $e^{\ln(8)} = 8$ and we know that $\ln(8)$ equals $2.07944$.

Verify and Summarize

• We can verify this by calculating $e^{2.07944}$ to check if it approximates $8$.

Final Answer

Thus, the exponential form of $\ln(8) = 2.07944$ is: $e^{2.07944} = 8$