Question

use natural logarithms to solve the equation. round to the nearest thousandth. show work!! 5e^(2x+11) =30

Answer 1

To solve the equation 5e^(2x+11) = 30 using natural logarithms, take the natural logarithm of both sides. Rearrange the equation and then divide by 2 to solve for x , x = (ln(30) - ln(5) - 11)/2.

Step-by-step explanation:

To solve the equation 5e^(2x+11) = 30 using natural logarithms, we can take the natural logarithm of both sides. This will cancel out the exponential function. The natural logarithm of 30 is approximately 3.401. So, we have ln(5e^(2x+11)) = ln(30).

Using the property of logarithms, ln(ab) = ln(a) + ln(b), we can rewrite the equation as ln(5) + ln(e^(2x+11)) = ln(30). The natural logarithm of e is 1, so ln(e^(2x+11)) = 2x+11.

Therefore, we have ln(5) + 2x + 11 = ln(30). Rearranging this equation, we get 2x = ln(30) - ln(5) - 11. Finally, divide both sides by 2 to solve for x: x = (ln(30) - ln(5) - 11)/2.

Answer 2

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