LOGARITHMS Flashcards
WHAT IS A LOGARITHM?
ANOTHER WORD FOR A POWER OR INDEX
EXAMPLES OF LOGARITHMS
- 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
WRITE 3² = 9 IN LOG.
- 2 = log₃ 9
- P = logᵦ A
RULES OF LOGARITHMS
x = BASE
WHAT CAN THE BASE 10 BE WRITTEN AS?
- WHEN THE BASE IS 10, LOG CAN BE ABBREVIATED AS Lg.
- Log₁₀ 100 = 2
- Lg100 = 2
WRITE 4² = 16 AS A LOGARITHM
Log₄ 16 = 2
WRITE 10³ = 1000 AS A LOGARITHM
Lg 1000 = 3
Log₁₀ 1000 = 3
WRITE Log₃ 81 = 4 AS AN EXPONENT
3⁴ = 81
WRITE Log₅ 3125 = 5 AS AN EXPONENT
5⁵ = 3125
LOGARITHMIC SCALE
WHAT ARE LOGARITHMIC SCALES USEFUL FOR?
- COMPARING QUANTITIES THAT HAVE A WIDE RANGE OF VALUES
- QUANTIFY SOUND INTENSITY
LOGARITHMIC SCALE
WHY IS THE LOGARITHMIC SCALE USED TO QUANTIFY SOUND?
BECAUSE IT HAS A VERY LARGE RANGE OF VALUES ON A LINEAR SCALE.
LOGARITHMIC SCALE
WHAT IS THE LOGARITHMIC SCALE FOR SOUND CALLED?
DECIBEL SCALE
LOGARITHMIC SCALE
WHAT IS THE LOWEST SOUND THAT CAN BE HEARD BY A HUMAN EAR?
10⁻¹² W/m²
LOGARITHMIC SCALE
WHAT IS THE THRESHOLD OF PAIN?
- IT IS REACHED AT
- 1 W/m²
- WHICH RANGES FROM
- 0.000000000001 - 1
- THIS MAKES IT DIFFICULT TO WORK WITH ON A GRAPH
LOGARITHMIC SCALE
HOW CAN THE INTENSITY LEVEL IN dB BE REPRESENTED?
B
LOGARITHMIC SCALE
HOW CAN DECIBELS BE REPRESENTED IN LOGARITHM FORMAT?
- Intensity Level B = 10Log10(I/Iₒ)
- IN DECIBELS
- Iₒ = 10⁻¹² w/m² (LIMIT OF HUMAN HEARING)
- I = INTENSITY OF SOUND BEING MEASURED
LOGARITHMIC SCALE
10 - 30 dB
QUIET
LOGARITHMIC SCALE
40 - 70 dB
SOUND STARTED TO LOUD LEVELS
LOGARITHMIC SCALE
80 - 100 dB
THE SOUND AT DANGEROUS NOISE LEVELS
LOGARITHMIC SCALE
110 - 135 dB
MOST DANGEROUS NOISE LEVELS
LOGARITHMIC SCALE
WHAT IS THE INTENSITY IN w/m² OF A SOUND WITH AN INTENSITY LEVEL OF 90 DECIBELS?
- 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
LOGARITHMIC SCALE
WARNING OF SOUNDS ABOVE 90dB
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
ALGEBRA KEY FACTS
WHAT IS A KEY FACT ABOUT LINEAR EQUATIONS?
THE APPEARANCE OF THE EQUATION MAY CHANGE BUT THE VALUES ON EACH SIDE REMAIN EQUAL.
ALGEBRA KEY FACTS
WHAT HAPPENS IF YOU DO THE OPPOSITE FUNCTION TO A VALUE ON EACH SIDE?
IT WILL REMOVE IT
ALGEBRA KEY FACTS
HOW DO YOU KNOW WHEN THE LINEAR EQUATION IS SOLVED?
WHEN THERE IS A LETTER VALUE ON ITS OWN?
ALGEBRA KEY FACTS
WHAT NUMBERING SYSTEMS ARE USED IN ENGINEERING?
DECIMAL
BINARY
OCTAL
HEXADECIMAL
ALGEBRA KEY FACTS
WHAT ARE SIMULTANEOUS EQUATIONS?
PAIRS OF EQUATIONS THAT MUST BE SOLVED TOGETHER
ALGEBRA KEY FACTS
HOW MANY SOLUTIONS DO QUADRATIC EQUATIONS HAVE?
TWO SOLUTIONS
ONE OF THE SOLUTIONS MAY BE ZERO
ALGEBRA KEY FACTS
HOW ARE QUADRATIC EQUATIONS SOLVED?
BY FACTORISING
USING THE QUADRATIC FORMULAE
ALGEBRA KEY FACTS
WHAT IS A LOGARITHM?
ANOTHER WAY TO DESCRIBE A INDICE OR A POWER
