Evaluating a Logarithm with Base 10

The teacher begins by apologizing for not covering a topic in the previous class. The lesson focuses on understanding logarithms, particularly when no base is specified, assuming it to be base 10. The teacher explains how to evaluate logarithms by rewriting them in exponential form. An example problem is solved using the one-to-one property, demonstrating how to equate exponents with the same base to find the value of a variable.

What is the assumed base of a logarithm if no base is specified?

• Base 10

• Base 5

• Base e

• Base 2

What does a logarithm ask when you see a base and a number?

• What is the base multiplied by the number?

• What is the difference between the base and the number?

• What is the base raised to what power to get the number?

• What is the sum of the base and the number?

How can you simplify the process of evaluating a logarithm?

• By rewriting it in exponential form

• By converting it into a division problem

• By adding the base and the number

• By subtracting the base from the number

What is the one-to-one property of exponents?

• If two exponents have the same base, their powers are equal

• If two exponents have the same power, their bases are equal

• If two exponents have different bases, their powers are equal

• If two exponents have different powers, their bases are equal

What is the value of X if 10 raised to X equals 10,000?

• 2

• 3

• 4

• 5