Solving Logarithmic Equations with One Log

The video tutorial covers solving logarithmic equations, starting with an introduction to the properties of logarithms. It provides step-by-step examples, including solving basic logarithmic equations, handling negative exponents, condensing multiple logarithms, and solving quadratic equations derived from logarithmic expressions. The importance of checking for extraneous solutions is emphasized throughout the tutorial.

What is a logarithmic equation?

• An equation with a logarithmic expression that contains a variable.

• An equation with a trigonometric expression that contains a variable.

• An equation with a polynomial expression that contains a variable.

• An equation with an exponential expression that contains a variable.

What is the first step in solving a logarithmic equation?

• Condense one side to a single logarithm using properties of logs.

• Convert to exponential form.

• Check for extraneous solutions.

• Rewrite the equation.

Why is it important to check for extraneous solutions?

• To ensure the solution does not create the log of a negative number.

• To ensure the solution is an integer.

• To ensure the solution is a positive number.

• To ensure the solution is a rational number.

In Example 1, what is the value of x when solving 4^3 = x - 1?

• 66

• 65

• 64

• 63

In Example 1, why is the solution x = 65 valid?

• Because 65 is a rational number.

• Because log base 4 of 64 is a positive value.

• Because 65 is an integer.

• Because 65 is a positive number.

In Example 2, what is 2 to the power of -2?

• 1/2

• 1/4

• 2

• 4

In Example 2, what is the value of x when solving 2^-2 = x/8?

• 4

• 3

• 2

• 1

In Example 3, what is the condensed form of log(x) + log(4)?

• log(x + 4)

• log(x * 4)

• log(x / 4)

• log(4 - x)

In Example 4, what is the quadratic equation formed after condensing and simplifying log base 6 of x + log base 6 of (x + 5) = 2?

• x^2 - 5x - 36 = 0

• x^2 - 5x + 36 = 0

• x^2 + 5x + 36 = 0

• x^2 + 5x - 36 = 0

In Example 4, which solution is valid after checking for extraneous solutions?

• x = -4

• x = 9

• x = 4

• x = -9