LOGARITHMS Flashcards
1
Q
WHAT IS A LOGARITHM?
A
ANOTHER WORD FOR A POWER OR INDEX
2
Q
EXAMPLES OF LOGARITHMS
A
- logᵦA = P
- Bᴾ = A
- 2³ = 8
- 3 = log₂ 8
- P = logᵦ A
- THREE IS THE POWER TO TWO WHICH MUST BE RAISED TO GIVE EIGHT
- THREE IS THE LOGARITHM (POWER)
- TWO IS THE BASE
- EIGHT IS THE ANSWER
3
Q
WRITE 3² = 9 IN LOG.
A
- 2 = log₃ 9
- P = logᵦ A
4
Q
RULES OF LOGARITHMS
A
x = BASE
5
Q
WHAT CAN THE BASE 10 BE WRITTEN AS?
A
- WHEN THE BASE IS 10, LOG CAN BE ABBREVIATED AS Lg.
- Log₁₀ 100 = 2
- Lg100 = 2
6
Q
WRITE 4² = 16 AS A LOGARITHM
A
Log₄ 16 = 2
7
Q
WRITE 10³ = 1000 AS A LOGARITHM
A
Lg 1000 = 3
Log₁₀ 1000 = 3
8
Q
WRITE Log₃ 81 = 4 AS AN EXPONENT
A
3⁴ = 81
9
Q
WRITE Log₅ 3125 = 5 AS AN EXPONENT
A
5⁵ = 3125
10
Q
LOGARITHMIC SCALE
WHAT ARE LOGARITHMIC SCALES USEFUL FOR?
A
- COMPARING QUANTITIES THAT HAVE A WIDE RANGE OF VALUES
- QUANTIFY SOUND INTENSITY
11
Q
LOGARITHMIC SCALE
WHY IS THE LOGARITHMIC SCALE USED TO QUANTIFY SOUND?
A
BECAUSE IT HAS A VERY LARGE RANGE OF VALUES ON A LINEAR SCALE.
12
Q
LOGARITHMIC SCALE
WHAT IS THE LOGARITHMIC SCALE FOR SOUND CALLED?
A
DECIBEL SCALE
13
Q
LOGARITHMIC SCALE
WHAT IS THE LOWEST SOUND THAT CAN BE HEARD BY A HUMAN EAR?
A
10⁻¹² W/m²
14
Q
A
14
Q
LOGARITHMIC SCALE
WHAT IS THE THRESHOLD OF PAIN?
A
- IT IS REACHED AT
- 1 W/m²
- WHICH RANGES FROM
- 0.000000000001 - 1
- THIS MAKES IT DIFFICULT TO WORK WITH ON A GRAPH
