Solving Logarithmic Equations in Algebra II

The video tutorial explains how to solve the equation 4 = log base b of 81 by converting it into an exponential form, b^4 = 81. It demonstrates the process of finding the base b by identifying that 3^4 equals 81, thus b equals 3. The tutorial also touches on fractional exponents, showing that raising both sides of the equation to the 1/4 power confirms that b is 3. The key takeaway is understanding the relationship between logarithms and exponents.

What does the equation 4 = log base b of 81 imply?

• b raised to the power of 81 equals 4

• 81 raised to the power of b equals 4

• b raised to the power of 4 equals 81

• 4 raised to the power of b equals 81

How can the equation b^4 = 81 be rewritten?

• As a polynomial equation

• As a logarithmic equation

• As a quadratic equation

• As a linear equation

What is the square root of 81?

• 10

• 7

• 8

• 9

Which number, when multiplied by itself four times, equals 81?

• 4

• 3

• 5

• 2

What is 3 to the fourth power?

• 243

• 27

• 54

• 81

How can 9 squared be expressed in terms of base 3?

• 3^5

• 3^4

• 3^3

• 3^2

What is the value of 81 raised to the 1/4 power?

• 3

• 2

• 5

• 4

What does raising both sides of the equation b^4 = 81 to the 1/4 power achieve?

• It simplifies the equation to b = 27

• It simplifies the equation to b = 9

• It simplifies the equation to b = 3

• It simplifies the equation to b = 81

What is the main concept behind logarithms as explained in the video?

• Logarithms are used to find the square root of a number

• Logarithms are used to solve quadratic equations

• Logarithms are used to find the power to which a base must be raised to get a certain number

• Logarithms are used to solve linear equations

What is the base b in the equation 4 = log base b of 81?

• 5

• 3

• 2

• 4