Logarithms

Question 1

What stays the same when converting between exponential and logarithmic form?

Answer 1

The base stays the same.

e^x = 5 => ln5 = x

Question 2

What is log of one always?

Answer 2

0

Question 3

What is log x of x always?

Answer 3

1

Question 4

What happens when you add two logs?

Answer 4

The insides are multiplied.

Question 5

What happens when you subtract logs?

Answer 5

The insides divide

Question 6

What can be done to an exponent that is on the inside of a log?

Answer 6

It can be multiplied to the front of the log.

Question 7

What can be done if the base of a log is a fraction?

Answer 7

The fraction can be reciprocated, this causes the sign to change.

Question 8

What must be done when moving a log to the denominator of a fraction?

Answer 8

The base and inside of the log must switch

Question 9

What happens when placing a log with the same base the exponent in the exponent?

Answer 9

The log and exponent “cancel” and the inside of the log is left over.

Question 10

What can be done if there are two logs one the numerator and one in the denominator of a fraction with the same base?

Answer 10

They can be turned into a single logarithm where the denominator’s inside is the base and the numerators inside stays the inside.