Question

Use natural logarithms to solve the equation. Round to the nearest thousandth 5e^(2x+11)=30

Answer 1

Answer: About -4.604.

Explanation:

To solve, we will isolate the x variable.

Given:

`5e^((2x+11))=30`

Divide both sides of the equation by 5:

`e^((2x+11))=6`

Natural log of both sides:

`Ln(e^((2x+11)))=Ln(6)`

Power property:

(2x + 11)(Lne) = Ln(6)

Simplify:

➜
`Lne = Log_ee = 1`

2x + 11 = Ln(6)

Subtract 11 from both sides of the equation:

2x = Ln(6) - 11

Divide both sides of the equation by 2:

`\displaystyle x=(Ln(6) - 11)/(2)`

Compute:

x = -4.60412 ≈ -4.604