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$x = \\frac{3}{\\ln 3}$
Answer
Explanation:
Step1: Isolate the exponential term
Add 4 to both sides of the equation (5e^{2x}-4 = 11):
(5e^{2x}=11 + 4)
(5e^{2x}=15)
Step2: Solve for (e^{2x})
Divide both sides by 5:
(e^{2x}=\frac{15}{5})
(e^{2x}=3)
Step3: Take the natural logarithm
Take (\ln) of both sides:
(\ln(e^{2x})=\ln(3))
Using the logarithm property (\ln(e^a)=a), we get:
(2x=\ln(3))
Step4: Solve for (x)
Divide both sides by 2:
(x=\frac{\ln(3)}{2})