Solving Exponential Equations

The video tutorial explains how to solve an exponential equation using logarithms. It begins by isolating the exponential part of the equation and then demonstrates how to convert it into a logarithmic form. The tutorial provides both exact and approximate solutions for the variable x and concludes by verifying the solution through substitution.

What is the first step in solving the exponential equation 10^x - 10 = 6?

• Subtract 10 from both sides

• Add 10 to both sides

• Multiply both sides by 10

• Divide both sides by 10

After isolating the exponential term, what is the next step?

• Add 7 to both sides

• Subtract 7 from both sides

• Multiply both sides by 7

• Divide both sides by 7

What is the base of the common logarithm?

• e

• 10

• 2

• 5

How do you express 10^x = 16/7 in logarithmic form?

• log(x) = 16/7

• x = log(10)

• log(16/7) = x

• x = log(7/16)

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

• 0.5360

• 0.3590

• 0.3950

• 0.9350

Why is it unnecessary to write the base for a common logarithm?

• Because it is always base 10

• Because it is always base e

• Because it is always base 5

• Because it is always base 2

What is the purpose of verifying the solution by substitution?

• To check if the solution satisfies the original equation

• To simplify the equation further

• To find a different solution

• To change the base of the logarithm

What should the left side of the equation equal after substitution?

• 6

• 16

• 7

• 10

What operation is performed to verify the solution?

• Division

• Subtraction

• Addition

• Multiplication

What is the final step in solving the exponential equation?

• Finding the exact solution

• Approximating the solution

• Verifying the solution

• Changing the base