which value of x makes the equation 4e³ˣ = 16 true?\nln 5/4\nln(4/3)\n1/4ln 2\n1/12ln 16\n1/4ln 5\n1/20ln…

Explanation:

Step1: Isolate the exponential term

Divide both sides of the equation $4e^{3x}=16$ by 4. We get $e^{3x}=\frac{16}{4}=4$.

Step2: Apply natural - logarithm to both sides

Since $y = e^x$ and $y=\ln x$ are inverse functions, taking the natural - logarithm of both sides of $e^{3x}=4$ gives $\ln(e^{3x})=\ln(4)$.

Step3: Use the property of logarithms

By the property $\ln(e^a)=a$, we have $3x=\ln(4)$.

Step4: Solve for x

Divide both sides of the equation $3x = \ln(4)$ by 3. So $x=\frac{1}{3}\ln(4)$.

Answer:

$\frac{1}{3}\ln 4$