logarithms back to numbers in Excel?


Bernard Liengme

The definition of log (base 10) is:
If x = 10^y then we say LOG(x) =y
Example: 100 = 10^2 so LOG(100)=2
It follows that if I know y and want x I use x = 10^y
If I know the log of x is 2, then x = 10^2 = 100

The definition of LN (base e) is:
If x = e^y (which can also be written as x=EXP(y)) then we say LN(x) =y
Example: 3 = e^1.096 so LOG(3)=1.096
It follows that if I know y and want x I use x = e^y
If I know LN(x) = 1.096 then x = EXP(1.906) which works out to be 3

best wishes


Very helpful, thank you Bernard. But is there a function in Excel that I can
use for a column of many figures?

Kind regards


i need to know the reverse of a log10 funtion to get back to the number.

If A1 contains the result of your LOG10 formula (e.g., =LOG10(1.234)),
then the antilog is =10^A1.

Although that does return exactly 1.234 in that case, in general do
not expect the antilog to exactly equal the parameter of LOG10. For
example, if A1 is =LOG10(PI()), =10^A1-PI()=0 is FALSE(!) [1].

Also, do not expect the antilog to exactly match mathematical
equalities. For example, if A1 is =LOG10(4.5)+LOG10(2) [2], =10^A1=9
is FALSE(!).

Infinitesimal differences are due to the limitations of computer
arithmetic as well as to the fact that generally LOG10 and the power
operator (^) use generating functions or algorithms to approximate
their results (when the exponent is non-integer in the case of the
power operator).


[1] But =10^A1=PI() is TRUE. The difference is due to Excel
heuristics which try to hide inequalities when the difference is
"close" to zero.

[2] We expect LOG10(4.5)+LOG10(2) = LOG10(4.5*2) = LOG10(9) based on
mathematical equalities.
Feb 4, 2020
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Dear sir,
I need to convert Average log e value to log10 value.
For example I have data (Avg log e value -450).
How can I convert this data to log10 value?

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