Solving Exponential Equations

The video tutorial explains how to solve an exponential equation by isolating the exponential part, converting it to a logarithmic equation, and solving for the variable x. The process involves using natural logarithms and verifying the solution through substitution and calculation. The tutorial also provides a decimal approximation of the solution and checks the accuracy using a calculator.

What is the first step in solving the equation 8 * e^x - 6 = 17?

• Multiply both sides by 8

• Add 6 to both sides

• Subtract 6 from both sides

• Divide both sides by 8

After isolating e^x, what is the next step in solving the equation?

• Multiply both sides by 8

• Subtract 8 from both sides

• Take the square root of both sides

• Divide both sides by 8

What is the base of the natural logarithm used in the transformation?

• e

• 238

• 2

• 10

How is the exponential equation rewritten as a logarithmic equation?

• log base 238 of e equals x

• log base 2 of 238 equals x

• log base e of 238 equals x

• log base 10 of 238 equals x

What is the approximate decimal value of x to four decimal places?

• 1.0615

• 1.0516

• 1.0651

• 1.0561

What operation is used to verify the solution of the equation?

• Substitution

• Graphing

• Integration

• Differentiation

What is the result when e raised to the power of natural log 238 is simplified?

• 0

• 1

• e

• 238

What is the exact solution of the equation in terms of natural log?

• natural log of 8

• natural log of 17

• natural log of 238

• natural log of 23

How can the solution be verified using a calculator?

• By entering 8 * e^(natural log 23) - 6

• By entering 8 * e^(natural log 8) - 6

• By entering 8 * e^(natural log 238) - 6

• By entering 8 * e^x - 6

What are the two forms of the solution accepted in the directions?

• Exact and approximate

• Graphical and numerical

• Algebraic and graphical

• Numerical and symbolic