Understanding Logarithms and the Change of Base Formula

The video tutorial explains how to evaluate logarithmic expressions using the change of base formula. It demonstrates the process with examples, showing how to use both common and natural logs to calculate logarithms on a calculator. The tutorial includes examples of calculating log base 3 of 9, log base 5 of 62, and log base 2 of 15, highlighting the importance of rounding and verifying results.

What is the purpose of using the change of base formula in logarithms?

• To simplify complex logarithmic expressions

• To evaluate logarithms using a calculator

• To find the derivative of logarithmic functions

• To convert logarithms into exponential form

Which two types of logarithms are commonly used in the change of base formula?

• Binary and decimal logs

• Trigonometric and hyperbolic logs

• Common and natural logs

• Exponential and polynomial logs

How can you evaluate log base 3 of 9 using the change of base formula?

• By adding common log 9 and common log 3

• By subtracting common log 3 from common log 9

• By multiplying common log 9 by common log 3

• By dividing common log 9 by common log 3

What is the result of log base 3 of 9 using the change of base formula?

• 2

• 1

• 3

• 4

When evaluating log base 5 of 62, why is rounding necessary?

• Because the result is an integer

• Because the result is a complex number

• Because the result is a repeating decimal

• Because the result is an irrational number

What is the approximate value of log base 5 of 62 rounded to four decimal places?

• 2.4653

• 2.5463

• 2.6543

• 2.5643

How do you verify the result of log base 5 of 62?

• By dividing 62 by 5

• By multiplying 5 by 62

• By raising 62 to the power of 5

• By raising 5 to the power of 2.5643

What is the approximate value of log base 2 of 15 using the change of base formula?

• 3.6099

• 3.9069

• 3.9609

• 3.6909

How can you verify the result of log base 2 of 15?

• By dividing 15 by 2

• By multiplying 2 by 15

• By raising 15 to the power of 2

• By raising 2 to the power of 3.9069

Why might the calculated value of log base 2 of 15 be slightly larger than 15?

• Because of rounding up

• Because of using a wrong base

• Because of rounding down

• Because of a calculation error