$$ \equiv 1 $$ Solve for $$ x $$. $$ \quad 4 \ln (2 x)=12 $$ Do not round any intermediate computations, and round your answer to the nearest hundredth. $$ x=\square $$

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UpStudy AI · Accepted Answer

1. Start with the equation:
   $$
   4 \ln(2x) = 12
   $$

2. Divide both sides by 4 to isolate the logarithm:
   $$
   \ln(2x) = \frac{12}{4} = 3
   $$

3. Exponentiate both sides to remove the natural logarithm:
   $$
   2x = e^3
   $$

4. Solve for $$ x $$ by dividing both sides by 2:
   $$
   x = \frac{e^3}{2}
   $$

5. Substitute the approximate value of $$ e^3 \approx 20.09 $$ (using $$ e^3 \approx 20.0855 $$) and divide by 2:
   $$
   x \approx \frac{20.0855}{2} \approx 10.04
   $$

Thus, the solution is:
$$
x \approx 10.04
$$
$$ x \approx 10.04 $$

Solve for .
Do not round any intermediate computations, and round your answer to the nearest hundredth.

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Solve for . Do not round any intermediate computations, and round your answer to the nearest hundredth.