Solving Exponential Equations

The video tutorial explains how to solve exponential equations using logarithms. It covers two examples: one involving a base of 9 and another with the natural base e. The process involves isolating the exponential part, applying logarithms, and solving for the variable. The tutorial emphasizes using a calculator for decimal approximations and verifies solutions by substituting back into the original equations.

What is the first step in solving an exponential equation with one exponential part?

• Add a constant to both sides

• Multiply both sides by a constant

• Take the square root of both sides

• Isolate the exponential part

In the equation 9^x + 34 = 94, what operation is performed to isolate 9^x?

• Divide both sides by 9

• Subtract 34 from both sides

• Add 34 to both sides

• Multiply both sides by 9

After isolating the exponential part, what is the next step in solving the equation?

• Add a constant to both sides

• Square both sides

• Multiply both sides by a constant

• Take the logarithm of both sides

What is the approximate value of x when solving 9^x = 60?

• 1.8634

• 3.1415

• 1.2345

• 2.4567

In the second example, what is the first step to isolate e^(2x)?

• Multiply both sides by 4

• Add 9 to both sides

• Divide both sides by 4

• Subtract 9 from both sides

What is the base of the natural logarithm used in the second example?

• 10

• 5

• e

• 2

What is the approximate value of x when solving e^(2x) = 14?

• 0.6931

• 3.1415

• 2.7182

• 1.3195

What property of logarithms allows the exponent to be moved to the front?

• Change of base property

• Power property

• Product property

• Quotient property

What is the natural log of e equal to?

• 1

• 0

• 10

• e

What should be the result of 4 * e^(2 * 1.3195) - 9?

• Approximately 60

• Exactly 40

• Approximately 47

• Exactly 50