Understanding the Change of Base Formula

The video tutorial explains the change of base formula for logarithms, which is useful when calculators do not support arbitrary bases. It demonstrates how to find log base 5 of 100 using the formula, converting it to log base 10 for calculation. The tutorial verifies the result and provides a detailed explanation of why the formula works, including a step-by-step derivation.

Why is the change of base formula particularly useful when using calculators?

• It is used for solving quadratic equations.

• It allows for easier multiplication.

• It helps in converting logarithms to a base that calculators can handle.

• It simplifies addition problems.

What does the change of base formula allow you to do with logarithms?

• Convert them into fractions.

• Change their base to any arbitrary base.

• Convert them into exponential equations.

• Solve them without a calculator.

In the change of base formula, what is typically used as the new base when using a calculator?

• Base 10 or base e

• Base 100

• Base 2

• Base 5

How do you express log base 5 of 100 using the change of base formula?

• log base 10 of 100 divided by log base 10 of 5

• log base 5 of 10 divided by log base 100 of 5

• log base 100 of 5 divided by log base 10 of 100

• log base 5 of 100 divided by log base 5 of 10

What is the approximate value of log base 5 of 100 calculated using the change of base formula?

• 2.500

• 2.000

• 2.861

• 3.000

Why does it make sense that 5 raised to the power of 2.861 is close to 100?

• Because 5 to the power of 2.861 is exactly 100.

• Because 5 to the power of 2.861 is between 5 squared and 5 cubed.

• Because 5 to the power of 3 is 100.

• Because 5 to the power of 2 is 100.

What is the result of raising 5 to the power of 2.861?

• 98

• 101

• 99.94

• 100

What is the first step in deriving the change of base formula?

• Setting the logarithm equal to a variable.

• Subtracting the bases.

• Adding the bases together.

• Multiplying both sides by the base.

In the derivation of the change of base formula, what property of logarithms is used?

• Logarithm of a sum

• Logarithm of a product

• Logarithm of a quotient

• Logarithm of a power

What does the change of base formula ultimately prove?

• Log base a of b is equal to log base x of b divided by log base x of a.

• Log base a of b is equal to log base a of x divided by log base b of x.

• Log base a of b is equal to log base b of a divided by log base x of a.

• Log base a of b is equal to log base x of a divided by log base x of b.