which of the following is the solution of $5e^{2x}-4 = 11$?\n$x=ln 3$\n$x=ln 27$\n$x=\frac{ln…

which of the following is the solution of $5e^{2x}-4 = 11$?\n$x=ln 3$\n$x=ln 27$\n$x=\frac{ln 3}{2}$\n$x=\frac{3}{ln 3}$

which of the following is the solution of $5e^{2x}-4 = 11$?\n$x=ln 3$\n$x=ln 27$\n$x=\frac{ln 3}{2}$\n$x=\frac{3}{ln 3}$

Answer

Explanation:

Step1: Isolate the exponential term

Add 4 to both sides of the equation $5e^{2x}-4 = 11$. $5e^{2x}=11 + 4=15$

Step2: Solve for $e^{2x}$

Divide both sides by 5. $e^{2x}=\frac{15}{5}=3$

Step3: Apply natural - logarithm

Take the natural - logarithm of both sides. Since $\ln(e^{a})=a$, we have $\ln(e^{2x})=\ln(3)$. $2x=\ln(3)$

Step4: Solve for $x$

Divide both sides by 2. $x = \frac{\ln(3)}{2}$

Answer:

$x=\frac{\ln3}{2}$