Question

Use natural logarithms to solve the equation. Round to the nearest thousandth. 7e^2x + 10 = 29

Answer 1

Answer:

  x ≈ 0.499

Step-by-step explanation:

The value of x can be found by undoing the operations done to it.

Solution

The operations done to the variable are ...

• multiply it by 2
• use that as the exponent with a base of e
• multiply the result by 7
• add 10

We undo these operations in reverse order:

  7e^(2x) + 10 = 29 . . . . given

  7e^(2x) = 19 . . . . . . . . . subtract 10

  e^(2x) = 19/7 . . . . . . . . . divide by 7

  2x = ln(19/7) . . . . . . . . take the natural logarithm

  x = (ln(19/7))/2 . . . . . . divide by 2

The rounded result is ...

  x ≈ 0.499