To solve the equation \( 0.86 = \ln(y) \), we recognize that \( \ln(y) \) represents the natural logarithm of \( y \), which has a base of \( e \) (where \( e \approx 2.71828 \)).

The equation can be rewritten using the definition of a logarithm: if \( \ln(y) = 0.86 \), then \( y = e^{0.86} \).

Now, let's calculate \( e^{0.86} \):

\[
y = e^{0.86} \approx 2.71828^{0.86} \approx 2.36
\]

Therefore, the solution is:

\[
y \approx 2.36
\]

Would you like further details or have any questions?

Here are some related questions you might be interested in exploring:

1. How do you solve natural logarithmic equations with different coefficients?
2. What are the properties of natural logarithms, and how do they apply to solving equations?
3. How can natural logarithms be used to model exponential growth or decay?
4. What is the inverse function of the natural logarithm, and how is it used?
5. How do you differentiate and integrate functions involving natural logarithms?

**Tip:** The natural logarithm \( \ln(y) \) is commonly used in calculus and real-world applications involving growth rates, such as in biology, finance, and physics.

Learn how to solve the equation ln(y) = 0.86 step-by-step. Understand the definition of natural logarithms and exponential functions with a detailed example. Suitable for advanced high school students.

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