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Logarithm (log). How do we know that 10 log 10 1000 = 10 x 3 ? Logarithmic and Exponential Functions Logarithmic and exponential functions are inverses of each other: If y = log b x then x = b y In words, log b x is the exponent you put on base b to get x . lol So,

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logarithm log
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.

example
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 1/31.62=0.0316 W

Logarithm:if b = logax then x = ab

1.5 = log10P1/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.