Compute the value of $x$ given:
\[
21 \cdot e^{3 x}=74
\]

Answer

Expert–verified

Hide Steps

Answer

Final Answer: The value of $x$ is $\boxed{0.42}$ (rounded to two decimal places).

Steps

Step 1 ：Given the equation $21 \cdot e^{3 x}=74$

Step 2 ：Divide both sides by 21 to isolate $e^{3x}$, giving us $e^{3x} = \frac{74}{21}$

Step 3 ：Take the natural logarithm of both sides to isolate $3x$, resulting in $3x = ln(\frac{74}{21})$

Step 4 ：Finally, divide both sides by 3 to solve for $x$, yielding $x = \frac{ln(\frac{74}{21})}{3}$

Step 5 ：Computing the above expression gives us a numerical value for $x$

Step 6 ：Final Answer: The value of $x$ is $\boxed{0.42}$ (rounded to two decimal places).