Respuesta :
Answer:
x = -4.604
Step-by-step explanation:
Here, we want to get the value of x
We start by dividing through by 5
e^(2x + 11) = 30/5
e^(2x + 11) = 6
Writing this in natural logarithm form, we have;
ln 6 = 2x + 11
2x + 11 = 1.792
2x = 1.792-11
2x = -9.208
x = -9.208/2
x = -4.604
The value of x from the given equation is
x=-4.604
Given :
[tex]5e^{2x+11} =30[/tex]
To solve for x , we need to get exponent 'e' alone
First we divide both sides by 5
[tex]e^{2x+11} =6[/tex]
Now we write the given exponent in logarithmic form
Lets take ln on both sides
[tex]lne^{2x+11} =ln6\\(2x+11)lne=ln(6)\\[/tex]
The value of ln(e) is 1
[tex](2x+11)=ln(6)\\2x+11=ln(6)\\subtract \; 11 \; on \; both \; sides\\2x=ln(6)-11\\Divide \; both \; sides \; by \; 2\\x=\frac{ln(6)-11}{2} \\x=-4.60412[/tex]
The value of x from the given equation is
x=-4.604
Learn more : brainly.com/question/185913
