LOGARITHMS

Question 1

WHAT IS A LOGARITHM?

Answer 1

ANOTHER WORD FOR A POWER OR INDEX

Question 2

EXAMPLES OF LOGARITHMS

Answer 2

• 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

Question 3

WRITE 3² = 9 IN LOG.

Answer 3

• 2 = log₃ 9
• P = logᵦ A

Question 4

RULES OF LOGARITHMS

Answer 4

x = BASE

Question 5

WHAT CAN THE BASE 10 BE WRITTEN AS?

Answer 5

• WHEN THE BASE IS 10, LOG CAN BE ABBREVIATED AS Lg.
• Log₁₀ 100 = 2
• Lg100 = 2

Question 6

WRITE 4² = 16 AS A LOGARITHM

Answer 6

Log₄ 16 = 2

Question 7

WRITE 10³ = 1000 AS A LOGARITHM

Answer 7

Lg 1000 = 3
Log₁₀ 1000 = 3

Question 8

WRITE Log₃ 81 = 4 AS AN EXPONENT

Answer 8

3⁴ = 81

Question 9

WRITE Log₅ 3125 = 5 AS AN EXPONENT

Answer 9

5⁵ = 3125

Question 10

LOGARITHMIC SCALE

WHAT ARE LOGARITHMIC SCALES USEFUL FOR?

Answer 10

• COMPARING QUANTITIES THAT HAVE A WIDE RANGE OF VALUES
• QUANTIFY SOUND INTENSITY

Question 11

LOGARITHMIC SCALE

WHY IS THE LOGARITHMIC SCALE USED TO QUANTIFY SOUND?

Answer 11

BECAUSE IT HAS A VERY LARGE RANGE OF VALUES ON A LINEAR SCALE.

Question 12

LOGARITHMIC SCALE

WHAT IS THE LOGARITHMIC SCALE FOR SOUND CALLED?

Answer 12

DECIBEL SCALE

Question 13

LOGARITHMIC SCALE

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

Answer 13

10⁻¹² W/m²

Question 14

LOGARITHMIC SCALE

WHAT IS THE THRESHOLD OF PAIN?

Answer 14

• IT IS REACHED AT
• 1 W/m²
• WHICH RANGES FROM
• 0.000000000001 - 1
• THIS MAKES IT DIFFICULT TO WORK WITH ON A GRAPH

Question 15

LOGARITHMIC SCALE

HOW CAN THE INTENSITY LEVEL IN dB BE REPRESENTED?

Answer 15

B

Question 16

LOGARITHMIC SCALE

HOW CAN DECIBELS BE REPRESENTED IN LOGARITHM FORMAT?

Answer 16

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

Question 17

LOGARITHMIC SCALE

10 - 30 dB

Answer 17

QUIET

Question 18

LOGARITHMIC SCALE

40 - 70 dB

Answer 18

SOUND STARTED TO LOUD LEVELS

Question 19

LOGARITHMIC SCALE

80 - 100 dB

Answer 19

THE SOUND AT DANGEROUS NOISE LEVELS

Question 20

LOGARITHMIC SCALE

110 - 135 dB

Answer 20

MOST DANGEROUS NOISE LEVELS

Question 21

LOGARITHMIC SCALE

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

Answer 21

• 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

Question 22

LOGARITHMIC SCALE

WARNING OF SOUNDS ABOVE 90dB

Answer 22

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

Question 23

ALGEBRA KEY FACTS

WHAT IS A KEY FACT ABOUT LINEAR EQUATIONS?

Answer 23

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

Question 24

# ALGEBRA KEY FACTS WHAT HAPPENS IF YOU DO THE OPPOSITE FUNCTION TO A VALUE ON EACH SIDE?

Answer 24

IT WILL REMOVE IT

Question 25

# ALGEBRA KEY FACTS HOW DO YOU KNOW WHEN THE LINEAR EQUATION IS SOLVED?

Answer 25

WHEN THERE IS A LETTER VALUE ON ITS OWN?

Question 26

# ALGEBRA KEY FACTS WHAT NUMBERING SYSTEMS ARE USED IN ENGINEERING?

Answer 26

DECIMAL BINARY OCTAL HEXADECIMAL

Question 27

# ALGEBRA KEY FACTS WHAT ARE SIMULTANEOUS EQUATIONS?

Answer 27

PAIRS OF EQUATIONS THAT MUST BE SOLVED TOGETHER

Question 28

# ALGEBRA KEY FACTS HOW MANY SOLUTIONS DO QUADRATIC EQUATIONS HAVE?

Answer 28

TWO SOLUTIONS ONE OF THE SOLUTIONS MAY BE ZERO

Question 29

# ALGEBRA KEY FACTS HOW ARE QUADRATIC EQUATIONS SOLVED?

Answer 29

BY FACTORISING USING THE QUADRATIC FORMULAE

Question 30

# ALGEBRA KEY FACTS WHAT IS A LOGARITHM?

Answer 30

ANOTHER WAY TO DESCRIBE A INDICE OR A POWER