Solving an exponentional equation by taking the natural log on both sides, 6 e^(-x) = 3

The video tutorial focuses on isolating the expression E raised to the negative X. It begins by dividing both sides of the equation by 6, then proceeds to eliminate the base E using the natural logarithm (Ln). The instructor demonstrates how to calculate the result, which is approximately 0.69, using a calculator. The process involves understanding the transformation of the equation and the use of logarithmic properties to solve for X.

What is the first step in isolating the term E raised to the negative X?

• Divide both sides by 6

• Add 6 to both sides

• Subtract 6 from both sides

• Multiply both sides by 6

Which mathematical operation is used to eliminate the base E in the equation?

• Division

• Natural logarithm

• Exponentiation

• Square root

After applying the natural logarithm, what does the equation simplify to?

• -X = -Ln(1/2)

• X = Ln(1/2)

• -X = Ln(1/2)

• X = -Ln(1/2)

What is the approximate value of X after calculation?

• -1.69

• -0.69

• 0.69

• 1.69

Why is the value of X considered approximate?

• Because it is a theoretical value

• Due to a calculation error

• Due to rounding during calculation

• Because it is an exact value