Logarithm (log)

1
Logarithm (log)

• How do we know that 10 log10 1000 10 x 3 ?
• Logarithmic and Exponential Functions
• Logarithmic and exponential functions are
  inverses of each other
• If y logbx then x by
• In words, logb x is the exponent you put on base
  b to get x. lol
• So,
• If x log10 1000 then 1000 10x
  and how much is x here? 10 to the power of
  what is equal to 1000? It would be 10 to the
  power of 3 (10x10x10) 1000.

2
Example

• If the power attenuation of a length of cable is
  given to be 15 dB, find the ratio of the
  input/output power
• 15 10log10 P1/P2
• 1.5 log10 P1/P2
• P1/P2 101.5 31.62
• P1/P2 31.62
• The calculation above illustrates that signals
  passing through this length of cable suffer a
  power attenuation by 31.62 times.
• If, for example, the input power is 1W, the power
  at the output of the cable would be
  1/31.620.0316 W
• Logarithm if b logax then x
  ab

1.5 log10 P1/P2 then P1/P2 101.5
Note when no base is indicated, it is assumed
(it means that) the base is 10. In other words,
log10P1/P2 and logP1/P2 is the same thing.