what is the solution to 3 + 4e^{x + 1}=11?\no x = ln2 - 1\no x = ln2 + 1\no x = \\frac{1}{e}\no x = \\frac{e…
what is the solution to 3 + 4e^{x + 1}=11?\no x = ln2 - 1\no x = ln2 + 1\no x = \\frac{1}{e}\no x = \\frac{e + 2}{e}
Answer
Explanation:
Step1: Isolate the exponential term
Subtract 3 from both sides of the equation $3 + 4e^{x + 1}=11$. $4e^{x + 1}=11 - 3=8$
Step2: Solve for the exponential part
Divide both sides by 4. $e^{x + 1}=\frac{8}{4}=2$
Step3: Use natural - logarithm property
Take the natural logarithm of both sides. Since $\ln(e^{a})=a$, we have $\ln(e^{x + 1})=\ln(2)$. $x + 1=\ln(2)$
Step4: Solve for x
Subtract 1 from both sides. $x=\ln(2)-1$
Answer:
$x=\ln2 - 1$