## 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.)