Questions: What is the solution to the equation e^x=331 ? x=

Transcript text: c. What is the solution to the equation $e^{x}=331$ ? $x=$ $\square$

Solution

Solution Steps

To solve these equations, we need to use logarithms and square roots. Here are the high-level ideas for each part:

a. To solve $ c^2 = 198 $, we take the square root of both sides. b. To solve $ e^2 = 198 $, we take the natural logarithm of both sides. c. To solve $ e^x = 331 $, we take the natural logarithm of both sides.

Step 1: Solving $ c^2 = 198 $

To solve $ c^2 = 198 $, we take the square root of both sides: \[ c = \sqrt{198} \] The numerical value is approximately: \[ c \approx 14.0712 \]

Step 2: Solving $ e^2 = 198 $

To solve $ e^2 = 198 $, we take the natural logarithm of both sides: \[ 2 = \ln(198) \] The numerical value is approximately: \[ 2 \approx 5.2883 \]

Step 3: Solving $ e^x = 331 $

To solve $ e^x = 331 $, we take the natural logarithm of both sides: \[ x = \ln(331) \] The numerical value is approximately: \[ x \approx 5.8021 \]

Final Answer

\[ \boxed{c \approx 14.0712} \] \[ \boxed{2 \approx 5.2883} \] \[ \boxed{x \approx 5.8021} \]

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