Find the solution of the exponential equation $$ 4 e^{x}=16 $$ in terms of logarithms, or correct to four decimal places. $$ x= $$

Question

UpStudy AI · Accepted Answer

1. Start with the equation:
   $$
   4e^x = 16
   $$

2. Divide both sides by $$4$$ to isolate $$ e^x $$:
   $$
   e^x = \frac{16}{4} = 4
   $$

3. Take the natural logarithm of both sides:
   $$
   \ln(e^x) = \ln(4)
   $$

4. Utilize the logarithm property $$\ln(e^x) = x$$:
   $$
   x = \ln(4)
   $$

5. To express $$ x $$ to four decimal places, evaluate:
   $$
   x \approx 1.3863
   $$
$$ x \approx 1.3863 $$

Find the solution of the exponential equation \( 4 e^{x}=16 \) in terms of logarithms, or correct to four decimal places. \( x= \)