Logarithms Part 2: Base Ten Logs, Natural Logs, and the Change-Of-Base Property

The video tutorial explains logarithmic bases, focusing on the common logarithm (base 10) and the natural base e. It describes how e is derived from interest calculations and its significance as an irrational number. The tutorial introduces natural logarithms, abbreviated as ln, and explains how to use them. It also covers the change of base property, which allows conversion of logarithms to different bases for easier calculation.

What is the base of the common logarithm used in practical applications like the pH scale?

• Base 2

• Base 5

• Base 10

• Base e

Which of the following is an irrational base commonly used in logarithms?

• Base e

• Base 1

• Base 2

• Base 10

What is the approximate value of the number e?

• 1.618

• 3.142

• 1.414

• 2.718

What is the abbreviation for the natural logarithm?

• le

• lg

• ln

• log

How can you express log base 5 of 15 using base 10?

• log base 15 of 5 / log base 15 of 10

• log base 10 of 5 / log base 10 of 15

• log base 5 of 15 / log base 5 of 10

• log base 10 of 15 / log base 10 of 5

What is the change of base property used for?

• To express logarithms in terms of a different base

• To solve logarithms with unknown bases

• To calculate the natural logarithm

• To convert logarithms to exponential form

If you want to convert log base 7 of x to natural logs, which expression would you use?

• ln(x) / ln(7)

• log base 10 of x / log base 10 of 7

• log base 7 of x / log base 7 of e

• ln(7) / ln(x)