Solving Exponential Equations with Logarithms

The video tutorial explains how to solve exponential equations using logarithms. It covers two examples: one with base 9 and another with base e. The process involves isolating the exponential part, applying logarithms, and solving for the variable. The tutorial emphasizes using natural logs for calculations and provides step-by-step solutions, including checking the results. The video concludes with a brief preview of the next example to be covered in the following video.

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

• Multiply both sides by a constant

• Add a constant to both sides

• Isolate the exponential part

• Take the logarithm of both sides

In the equation 9^x + 34 = 93, what operation is performed to isolate 9^x?

• Add 34 to both sides

• Subtract 34 from both sides

• Multiply both sides by 9

• Divide both sides by 9

After isolating 9^x, what is the next step to solve for x?

• Square both sides

• Take the natural log of both sides

• Multiply both sides by a constant

• Add a constant to both sides

What property of logarithms allows us to move the exponent to the front?

• Power property

• Change of base property

• Product property

• Quotient property

What is the approximate value of x in the equation 9^x = 60?

• 1.2345

• 1.8634

• 3.1415

• 2.4567

In the equation 4e^(2x) - 9 = 47, what is the first step to isolate e^(2x)?

• Subtract 9 from both sides

• Divide both sides by 4

• Add 9 to both sides

• Multiply both sides by 4

After isolating e^(2x), what is the next step to solve for x?

• Square both sides

• Take the natural log of both sides

• Add a constant to both sides

• Multiply both sides by a constant

What is the value of the natural log of e?

• 0

• 1

• e

• 2

What is the approximate value of x in the equation e^(2x) = 14?

• 1.2345

• 1.8634

• 1.3195

• 2.4567

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

• 70

• 50

• 47

• 60