Solving Exponential equations

The video tutorial explains how to solve an exponential equation of the form 4e^(-0.3x) - 7 = 13. The instructor demonstrates isolating the exponential term by using inverse operations, such as addition and division, to simplify the equation. The solution involves taking the natural logarithm of both sides to solve for x, resulting in x ≈ -5.36. Alternative methods for solving the equation are also discussed, emphasizing the use of logarithmic properties.

What is the first step in solving the equation 4e^(-0.3x) - 7 = 13?

• Multiply both sides by 4

• Add 7 to both sides

• Divide both sides by 4

• Subtract 7 from both sides

After isolating the exponential term, what is the next operation performed on the equation e^(-0.3x) = 5?

• Add 5 to both sides

• Subtract 5 from both sides

• Take the logarithm of both sides

• Multiply both sides by 5

Which method can be used to solve the equation after isolating the exponential term?

• Graphical method

• Elimination method

• Substitution method

• Logarithmic method

Which of the following is a correct conversion of the equation e^(-0.3x) = 5 into logarithmic form?

• ln(x) = -5

• ln(x) = 5

• ln(5) = 0.3x

• ln(5) = -0.3x

What is the approximate value of x when solving the equation 4e^(-0.3x) - 7 = 13?

• 3.36

• -5.36

• -3.36

• 5.36