Mastering Logarithmic Equations

The video tutorial covers solving logarithmic equations, starting with an introduction to the concept and moving through various strategies such as using the same base, changing forms between logarithmic and exponential, and applying logarithmic properties. The tutorial concludes with a real-world application of logarithms, demonstrating their use in modeling bacterial growth. Throughout the video, the instructor emphasizes the importance of checking solutions, especially when dealing with negative values.

What is the first step when solving logarithmic equations with the same base on both sides?

• Multiply the logarithms

• Set the arguments equal to each other

• Divide the logarithms

• Add the logarithms together

In the equation log base 12 of 4x equals log base 12 of 5x minus 10, what value of x makes the equation true?

• x = 1

• x = 2

• x = 10

• x = 5

When changing a logarithmic equation to exponential form, what is the base of the exponent?

• The coefficient of the logarithm

• The argument of the logarithm

• The exponent of the logarithm

• The base of the logarithm

In the equation log base 4 of 7x equals -2, what is the value of x?

• x = 1/16

• x = 1/7

• x = 1/4

• x = 1/112

What property allows you to combine log base 5 of x and log base 5 of (x + 6) into a single logarithm?

• Product Property

• Change of Base Property

• Quotient Property

• Power Property

Why can't you take the logarithm of a negative number?

• It results in an undefined value

• It results in zero

• It results in a negative value

• It results in a complex number

In the equation log base 6 of 10 divided by -4x equals log base 6 of 26, what is the value of x?

• x = -5/52

• x = -10/52

• x = -10/104

• x = -26

What is the domain of a logarithmic function?

• x ≥ 0

• x < 0

• x > 0

• x ≤ 0

In the bacterial growth example, how many hours are in 3 days?

• 96 hours

• 60 hours

• 48 hours

• 72 hours

What is the inverse of the equation y = 2^x?

• y = 2x

• y = x^2

• y = log base 2 of x

• y = log base 10 of x