Questions: Solve the logarithmic equation. 2+7 ln x=65 x=

Transcript text: Solve the logarithmic equation. \[ \begin{array}{l} 2+7 \ln x=65 \\ x=\square \end{array} \] (Simplify your answer. Type an exact answer, using $e$ as needed.)

Solution

Solution Steps

Step 1: Isolate the Logarithmic Term

Starting with the equation: \[ 2 + 7 \ln x = 65 \] we first isolate the logarithmic term by subtracting 2 from both sides: \[ 7 \ln x = 63 \]

Step 2: Solve for $ \ln x $

Next, we divide both sides by 7 to solve for $ \ln x $: \[ \ln x = 9 \]

Step 3: Convert to Exponential Form

To find $ x $, we convert the logarithmic equation to its exponential form: \[ x = e^9 \]

Final Answer

Thus, the exact value of $ x $ is: \[ \boxed{x = e^9} \]

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