## Conversion of Natural Logs to Base-10 Logs.

Some business calculators have *natural logarithm *functions
instead of *base-10 logarithms.* Many scientific calculators
have both. *Natural logarithms* use the number (*e = 2.7183...)
*as their base instead of the number *10*. The natural
logs and natural antilogs can be converted to base-10 counterparts
as follows:

Natural logs usually use the symbol *Ln* instead of *Log*.

Natural antilogs may be represented by symbols such as: InvLn,
Ln^(-1), e^x, or exp.

#### To convert a natural logarithm to base-10 logarithm, divide
by the conversion factor 2.303.

- For example, to calculate Log (100): if your calculator yields
*Ln(100) = 4.60517, *then* Log(100) = Ln(100)/2.303 = 4.60517/2.303
= 1.9996 (*very close to exact answer of* 2)*
*For example, to calculate Log(1.6210^-4), *if your calculator
yields *Ln(1.6210^-4) = -8.728* then* Log(1.6210^-4) =
Ln(1.6210^-4)/2.303 = -8.728/2.303 = -3.790 *(agrees with correct
answer)

#### To convert a natural antilog to a base=10 antilog, multiply
by the conversion factor 2.303 __before__ taking the natural
antilog..

- For example, to calculate the base-10 antilog of
* -3:*

Use your calculator to find* InvLn(-3*2.303) = InvLn(-6.909).
*Then *AntiLog(-3) = InvLn(-6.909) = 9.9910^-4 *(very
close to exact answer of *0.001)*
- For example, to calculate the base-10 antilog of
* -8.45:
*

Use your calculator to find* InvLn(-8.45*2.303) = InvLn(-19.460).
*Then* AntiLog(-8.45) = InvLn(-19.460) = 3.53610^-9 (*very
close to exact answer of *3.54810-9.)*

#### RETURN** to Logarithm Page.**