Questionn, using a calculator if necessary to evaluate the logarithm. Write your answer as a fraction or ro $\ln \left(\mathrm{e}^{\mathrm{x}}\right)=15.1$ w window) $x=$ $\square$

Studdy Solution

STEP 1

1. The equation involves the natural logarithm and the exponential function.
2. The natural logarithm $\ln$ and the exponential function $e^x$ are inverse functions.
3. We will use properties of logarithms to solve for $x$ .

STEP 2

1. Simplify the equation using properties of logarithms.
2. Solve for $x$ .

STEP 3

Use the property of logarithms that states $\ln(e^x) = x$ . This simplifies the equation:
$\ln(e^x) = 15.1$
This simplifies directly to:
$x = 15.1$

STEP 4

Since the equation is already simplified to $x = 15.1$ , there is no further calculation needed.
The value of $x$ is:
$\boxed{15.1}$

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