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, ex, 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(1.62x10-4),
if your calculator yields Ln(1.62x10-4)
= -8.728 then Log(1.62x10-4)
= Ln(1.62x10-4)/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
with a calculator providing only natural antilogs:
Use your calculator to find InvLn(-3*2.303) =
InvLn(-6.909). Then AntiLog(-3) = InvLn(-6.909) =
9.99x10-4 (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.