Solving Logarithmic Equations

The video tutorial explains how to solve logarithmic equations by isolating the logarithm, converting it to an exponential equation, and solving for the unknown variable. It covers three examples, each demonstrating the process of finding both exact and decimal solutions using a scientific calculator. The tutorial emphasizes the importance of isolating the logarithm and using the natural log base E for conversions.

What is the first step in solving a logarithmic equation?

• Multiply both sides by 2

• Isolate the logarithm

• Add a constant to both sides

• Convert to a quadratic equation

In the equation ln(5x + 4) = 9, what is the base of the logarithm?

• 10

• 5

• 2

• e

What is the exact solution for x in the equation ln(5x + 4) = 9?

• x = (e^9 / 4) * 5

• x = (e^9 * 4) / 5

• x = (e^9 - 4) / 5

• x = (e^9 + 4) / 5

What is the decimal approximation of x for ln(5x + 4) = 9 to four decimal places?

• 1618.8169

• 1619.8168

• 1618.8168

• 1619.8167

In the equation ln(3x) = 11, what operation is performed to isolate the logarithm?

• Add 7 to both sides

• Divide both sides by 3

• Subtract 7 from both sides

• Multiply both sides by 3

What is the exact solution for x in the equation ln(3x) = 11?

• x = e^11 / 3

• x = 3 / e^11

• x = e^11 * 3

• x = 3 * e^11

What is the decimal approximation of x for ln(3x) = 11 to four decimal places?

• 19958.0472

• 19957.0472

• 19958.0471

• 19957.0471

In the equation ln(2x + 3) = 6, what is the first step to isolate the logarithm?

• Add 3 to both sides

• Subtract 3 from both sides

• Divide both sides by 2

• Multiply both sides by 2

What is the exact solution for x in the equation ln(2x + 3) = 6?

• x = (e^6 + 3) / 2

• x = (e^6 - 3) / 2

• x = (e^6 * 3) / 2

• x = (e^6 / 3) * 2

What is the decimal approximation of x for ln(2x + 3) = 6 to four decimal places?

• 201.2144

• 202.2144

• 201.2143

• 202.2143