Questions: For f(x, y) = ln x + y^3, find f(e^5, 8).

Transcript text: For $f(x, y)=\ln x+y^{3}$, find $f\left(e^{5}, 8\right)$.

Solution

Step 1: Define the Function

The function is given by

\[ f(x, y) = \ln x + y^3 \]

Step 2: Substitute the Values

We need to evaluate $ f(e^5, 8) $. Substituting $ x = e^5 $ and $ y = 8 $ into the function gives:

\[ f(e^5, 8) = \ln(e^5) + 8^3 \]

Step 3: Simplify the Expression

Using the property of logarithms, $ \ln(e^a) = a $, we have:

\[ \ln(e^5) = 5 \]

Calculating $ 8^3 $:

\[ 8^3 = 512 \]

Thus, we can simplify the function:

\[ f(e^5, 8) = 5 + 512 = 517 \]

The value of $ f(e^5, 8) $ is

\[ \boxed{517} \]

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