RULES OF LOGARITHMS - Problem 2

Let a be a positive number such that a does not equal 1, let n be a real number, and let u and v be positive real numbers.

Logarithmic Rule 1:

Problem 2: Calculate .

Answer: 6

Solution: The problem can be worked two ways, as is, and expanded.

can be written because .

can also be written Log100+Log10+Log1000=2+1+3=6

Since the answers are the same, then is equivalent to Log100+Log10+Log1000

Note: The numbers 2, 1, 3, and 6 are the exponents. Log means the base is 10. Let's check the answer in terms of exponents.

, , , and .

If you would like to work another problem, click on Problem.