Change of Base Formula

What is the relationship between logarithms of different bases?

• Logarithms of different bases can be converted using the Change of Base Formula, allowing comparison and calculation.

• Logarithms of different bases cannot be compared or calculated directly.

• Logarithms of different bases are always equal to each other.

• Logarithms of different bases are only useful in specific mathematical contexts.

How do you convert log_3(9) using the Change of Base Formula?

• log(9) / log(3) = 2

• log(9) / log(2) = 3

• log(3) / log(9) = 0.5

• log(9) / log(4) = 1.5

How can you simplify log_4(64) using the Change of Base Formula?

• log(64) / log(4) = 2

• log(64) / log(4) = 4

• log(64) / log(4) = 3

• log(64) / log(4) = 5

What is the Change of Base Formula?

• log_b(a) = log_k(a) / log_k(b) for any positive k

• log_b(a) = log_k(b) / log_k(a) for any positive k

• log_b(a) = a / b

• log_b(a) = b / a

What is the value of log_10(1000) using the Change of Base Formula?

• 1

• 2

• 3

• 4

What is the significance of the Change of Base Formula in solving logarithmic equations?

• It allows for easier calculations and comparisons of logarithmic values across different bases.

• It simplifies the process of converting logarithmic equations into exponential form.

• It provides a method to solve for the variable in linear equations.

• It helps in determining the domain of logarithmic functions.

What does log_b(1) equal for any base b?

• 0

• 1

• b

• undefined

How do you express log_2(8) using the Change of Base Formula?

• log(8) / log(2) = 3

• log(2) / log(8) = 1/3

• log(8) / log(10) = 0.903

• log(2) / log(10) = 0.301

What is the base change for log_7(49)?

• 1

• 2

• 3

• 4

How do you express log_6(36) using the Change of Base Formula?

• log(36) / log(6) = 2

• log(36) / log(2) = 6

• log(6) / log(36) = 1/2

• log(36) / log(3) = 4