Logarithms and Exponential Functions

The video tutorial introduces the 10-base numeric system, explaining its natural basis due to human digits. It delves into logarithms, particularly log base-10, illustrating how to find the power of 10 that results in a given number. The concept of ceilings in logarithms is discussed, showing how to round up logarithmic values to the nearest whole number. The tutorial concludes with an exploration of powers of 10, demonstrating how the ceiling of logarithms for numbers between 11 and 100 is consistently 2.

Why is our natural number system based on the number 10?

• Because we have 10 toes

• Because it is the easiest number to calculate with

• Because it is a universal constant

• Because we have 10 fingers

What is the logarithm base 10 of 100?

• 2

• 1

• 10

• 100

Why do we not write the base 10 explicitly when dealing with logarithms?

• Because it is not necessary for calculations

• Because it is a universal rule

• Because it is the default base

• Because it is too complex

What is the ceiling of the logarithm base 10 of 50?

• 50

• 2

• 1.69897

• 1

What is 10 to the power of 3?

• 100

• 1000

• 10

• 10000

For which range of numbers is the ceiling of the logarithm always 2?

• 1001 to 10000

• 101 to 1000

• 11 to 100

• 1 to 10