Questions: Solve for x ln x = 4

Transcript text: Solve for $x$ \[ \ln x=4 \]

Solution

Solution Steps

To solve the equation $\ln x = 4$, we need to find the value of $x$ that satisfies this equation. The natural logarithm function $\ln$ is the inverse of the exponential function with base $e$. Therefore, we can exponentiate both sides of the equation to solve for $x$.

Step 1: Rewrite the Equation

We start with the equation given in the problem: \[ \ln x = 4 \]

Step 2: Exponentiate Both Sides

To solve for $x$, we exponentiate both sides of the equation using the base $e$: \[ x = e^4 \]

Step 3: Calculate the Value

Calculating $e^4$ gives us: \[ x \approx 54.5982 \]