logarithms

What is Logarithm?

A logarithm is the power to which a number must be raised in order to get some other number.

 

"opposite" of  exponential just as subtraction is the opposite if addition and division is the opposite of multiplication. Logs "undo" exponential. Technically speaking, log are the inverses of exponential.

For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100:

log 100 = 2

because,

10² = 100

Properties for Condensing Logarithms

Property 1: 0=log_a  1= Zero-Exponent Rule

Property 2: 1 = log_a a

Property 3: log_a x + log_a y log_a (xy) – Product Rule

Property 4: log_a x – log_a y = log_a (x/y) – Quantient Rule

Property 5: y log_a x = log_a x³ – Power Rule

Example : solve log(5x-11) = 2

log(5x-11) = 2

5x – 2 = 10²

5x- 2 = 100

X=102/5

Answer: log(5x-11) = 2 is x 102/5

Example : 
What is log₅(625)?

 "how many 5s need to be multiplied together to get 625?"
Solution: 5 × 5 × 5 × 5 = 625, so we need 4 of the 5s Answer: log₅(625) = 4

Example:

What is log2 (64)??

"how many 2s need to be multiplied together to get 64"?

Solution:

2 x 2 x 2 x 2 x 2 x 2 = 64, so we need 6 of the 2s

Log 2 (64) = 6

 

Question!

 

Log₄ (16) = 2

Log₈ (x) = 2

Log₈ (64) = x