LOGARITHMS Flashcards

1
Q

WHAT IS A LOGARITHM?

A

ANOTHER WORD FOR A POWER OR INDEX

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

WRITE 3² = 9 IN LOG.

A
  • 2 = log₃ 9
  • P = logᵦ A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

RULES OF LOGARITHMS

A

x = BASE

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

WRITE 4² = 16 AS A LOGARITHM

A

Log₄ 16 = 2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

WRITE 10³ = 1000 AS A LOGARITHM

A

Lg 1000 = 3
Log₁₀ 1000 = 3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

WRITE Log₃ 81 = 4 AS AN EXPONENT

A

3⁴ = 81

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

WRITE Log₅ 3125 = 5 AS AN EXPONENT

A

5⁵ = 3125

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

LOGARITHMIC SCALE

WHAT ARE LOGARITHMIC SCALES USEFUL FOR?

A
  • COMPARING QUANTITIES THAT HAVE A WIDE RANGE OF VALUES
  • QUANTIFY SOUND INTENSITY
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

LOGARITHMIC SCALE

WHAT IS THE LOGARITHMIC SCALE FOR SOUND CALLED?

A

DECIBEL SCALE

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

LOGARITHMIC SCALE

WHAT IS THE LOWEST SOUND THAT CAN BE HEARD BY A HUMAN EAR?

A

10⁻¹² W/m²

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q
A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

LOGARITHMIC SCALE

HOW CAN THE INTENSITY LEVEL IN dB BE REPRESENTED?

A

B

16
Q

LOGARITHMIC SCALE

HOW CAN DECIBELS BE REPRESENTED IN LOGARITHM FORMAT?

A
  • Intensity Level B = 10Log10(I/Iₒ)
  • IN DECIBELS
  • Iₒ = 10⁻¹² w/m² (LIMIT OF HUMAN HEARING)
  • I = INTENSITY OF SOUND BEING MEASURED
17
Q

LOGARITHMIC SCALE

10 - 30 dB

A

QUIET

18
Q

LOGARITHMIC SCALE

40 - 70 dB

A

SOUND STARTED TO LOUD LEVELS

19
Q

LOGARITHMIC SCALE

80 - 100 dB

A

THE SOUND AT DANGEROUS NOISE LEVELS

20
Q

LOGARITHMIC SCALE

110 - 135 dB

A

MOST DANGEROUS NOISE LEVELS

21
Q

LOGARITHMIC SCALE

WHAT IS THE INTENSITY IN w/m² OF A SOUND WITH AN INTENSITY LEVEL OF 90 DECIBELS?

A
  • B = 10 Log₁₀ I / Iₒ
  • B / 10 = Log₁₀ I / Iₒ
  • 10ᴮ/¹⁰ = I / Iₒ
  • I = Iₒ 10ᴮ/¹⁰
  • I = 10⁻¹² X 10⁹⁰/¹⁰
  • I = 10⁻¹² X 10⁹
  • I = 10⁻³ w/m²
22
Q

LOGARITHMIC SCALE

WARNING OF SOUNDS ABOVE 90dB

A

CAN PERMANENTLY DAMAGE HEARING IF EXPOSURE IS LONG ENOUGH
ALWAYS CHECK THE HEALTH AND SAFETY REQUIREMENTS IN AREAS WHERE THERE IS A RISK OF EXPOSURE TO LOUD NOISE
WEAR EAR PROTECTORS WHEN ADVISED

23
Q

ALGEBRA KEY FACTS

WHAT IS A KEY FACT ABOUT LINEAR EQUATIONS?

A

THE APPEARANCE OF THE EQUATION MAY CHANGE BUT THE VALUES ON EACH SIDE REMAIN EQUAL.

24
Q

ALGEBRA KEY FACTS

WHAT HAPPENS IF YOU DO THE OPPOSITE FUNCTION TO A VALUE ON EACH SIDE?

A

IT WILL REMOVE IT

25
Q

ALGEBRA KEY FACTS

HOW DO YOU KNOW WHEN THE LINEAR EQUATION IS SOLVED?

A

WHEN THERE IS A LETTER VALUE ON ITS OWN?

26
Q

ALGEBRA KEY FACTS

WHAT NUMBERING SYSTEMS ARE USED IN ENGINEERING?

A

DECIMAL
BINARY
OCTAL
HEXADECIMAL

27
Q

ALGEBRA KEY FACTS

WHAT ARE SIMULTANEOUS EQUATIONS?

A

PAIRS OF EQUATIONS THAT MUST BE SOLVED TOGETHER

28
Q

ALGEBRA KEY FACTS

HOW MANY SOLUTIONS DO QUADRATIC EQUATIONS HAVE?

A

TWO SOLUTIONS
ONE OF THE SOLUTIONS MAY BE ZERO

29
Q

ALGEBRA KEY FACTS

HOW ARE QUADRATIC EQUATIONS SOLVED?

A

BY FACTORISING
USING THE QUADRATIC FORMULAE

30
Q

ALGEBRA KEY FACTS

WHAT IS A LOGARITHM?

A

ANOTHER WAY TO DESCRIBE A INDICE OR A POWER