Logarithms

• Logarithms are an alternative way of expressing quantities that involve exponents.
• Fill in the blanks

  A) logarithm symbol

  B) base

  C) argument

  
• Fill in the blanks

  A) real numbers

  B) 1

  C) 0

  D) argument

  E) x

  F) b

  G) y

  
• transform exponential to logarithmic

  5^3=125

  A) 5

  B) 125

  C) = 3

  
• Common logarithms are logarithms with a base of 10. 
• In a common logarithm, we no longer need to write the “10” as the base. We leave it blank since it is already understood that we are dealing with a common logarithm.
• Natural logarithms use a “special number” as the base. This number is an irrational number represented as e. Formally, e is called Euler’s number (named after the mathematician Leonhard Euler). e is approximately equal to 2.718
• However, we do not write natural logarithms like your ordinary logarithms. We use the symbol “ln” instead of “log” and omit the base e. So, loge10 can be written as ln 10 (read as “natural logarithm of 10”). Another example: loge1 is equal to ln 1.
• Express log25 + log24 as a single logarithm.

  A) log

  B) 2

  C) 20

  
• Given that log 3 ≈ 0.48 and log 2 ≈ 0.30. What is the approximate value of log 6?

  A) 6

  B) 3

  C) 2

  D) 6

  E) 0.48

  F) 0.3

  G) 6

  H) 0.78

  
• Expand log4(7a(b + 4)) using the product property of logarithms.

  A) log 47th+log4a+log4b+4

  
• Fill in the blanks

  A) Product

  B) Quotient

  C) Power

  
• Expand the equation

  A) logx-1-log3

  
• Expand the equation

  A) 3loga

  
• Expand the equation

  A) 2lnj

  
• Expand it

  A) 2log4a+log4b

  
• Expand it

  A) 2lnx+3lny

  
• Expand it

  A) log3+2loga-log2+loga+b

  
• Simplify it

  A) 8x7

  B) 56

  
• Simplify it

  A) log34x2+20x

  B) log34x2+20x

  
• Simplify it

  A) log2a3b

  
• Answer it

  A) 5z=xy