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| logby = x is equivalent to bx=y | Definition of logarithm |
| logb1 = 0 | b0=1 |
| logbb = 1 | b1=b |
| logb0 = UNDEFINED | b-¥=0 |
| logbbx = x | Exponentials and logarithms are inverse functions |
| blogby = y (y>0) | Exponentials and logarithms are inverse functions |
| logbcd = logbc + logbd | Logarithms convert multiplication to addition |
| logb(c/d) = logbc - logbd | Logarithms convert division to subtraction |
| logbax = xlogba | Logarithms can be used to move a variable out of the exponent |
| logb(1/a) = logba-1 = -logba | For a base larger than 1, logs of numbers smaller than 1 are negative |
| log x = log10x | Shorthand for Common Log
(base = 10) |
| ln x = logex | Shorthand for Natural Log
(base = e) |
| logax = logbx/logba | You only need one log function to compute log to any base |
| logax = log x/log
a
logax = ln x/ln a |
Special cases of previous property using common log and natural log |
| logbx ==> LOG(x,b)
in Excel
log x ==> LOG(x) in Excel ln x ==> LN(x) in Excel |
Log function in Excel |
*These properties can be derived based on the definition of logarithm given at the top of this table.