What is a ‘logaritmo’?
log↓a(b) = C
A logarith helps us answers the question: does the power of one number have to be to get another number?
Basically:
log↓a(b) = C
a^c = b
For example:
log↓6(36)= x
6^2 = 36
x = 36
What does the same base law of logarithms state for subtraction and addition?
Addition:
It states that if two logarithms with the same base are being added, then they can be merged to become one logarithm, retaining the same base but the terms are multiplied together.
For example:
log↓2(4) + log↓2(8) = log↓2(4*8)
= log↓2(32)
Subtraction:
It states that if two logarithms with the same base are being subtracted, then they can be merged to become one logarithm, retaining the same base but the terms are divided.
For example:
log↓2(8) - log↓2(4) = log↓2(8÷4)
= log↓2(2)
= 1
What are the terms of the letters a and b in a logarithm?
log↓a(b) = C
a=base
b=term
What does the power law of logarithms state?
If the term has a power, it can become the logarithms coefficient.
For example:
log↓2(4^2) = 2log↓2(4)
What is the change of base law?
This law states that a logarithm’s base can be changed to any number by making it a divison following this structure:
log↓b(a)= log↓c(a) ÷ log↓c(b)
If there is no base written in a logarithm, e.g: log(100), what is the base?
If no base is written, the base is 10.
What is the natural logarithm?
The natural logarithm is represented with ln
ln = log↓e( ), where is the number: 2.718….
What is the answer to the following:
5^log↓5 (322)
It is 322. Why?
Because the answer to log↓5 (322) is the power of 5 that gets you 322. As that log is the power of 5, the answer is 25.
How would you write the number 1 as a log that has a base of 6?
log↓6 (6)
How would you write the number 3 as a log with a base of 4?
3log↓4 (4) which can also be written as: log↓4 (4^3)
