LOGARITHM

^{Definition of logarithm?}

logarithm is the exponent that indicates the power 
to which a base number is raised to produce a given number.

Logarithm is invented by John Napier.

Laws of logarithm

qLoga PQ = Loga P + Loga Q

q Loga P/Q = Loga P – Loga Q

q Loga Pn = nLoga P

q Loga 1 = 0

q Loga a = 1

q Loga y = Logb y / Logb a

Exponent and Base

Common logarithm base

Example: the base 10 logarithm of 100 is 2

Example 2: 2^x = 5  ^{(index form)}

• How to find ^x?
• Need to make sure that they are the same base

                    2^x = 5

^x = log₂ 5

Example 3:Find x, Log2 (5x + 7) = 5

5x + 7 = 2⁵

2⁵  is actually 2 x 2 x 2 x 2 x 2

5x + 7 = 32

5x = 32 – 7

5x = 25

X = 25/5

Anwser: X = 5

Questions that you can try:

1.Given: log₈(5) = b. Express log₄(10) in terms of b. 

2. Solve for x the equation 4^{x - 2} = 3^{x + 4}

3. Simplify without calculator: log₆(216) + [ log(42) - log(6) ] / log(49) 

GOODLUCK!😊😊😊