How to Calculate an Antilogarithm

The logarithm operation for a number aims to find the power to which the logarithm base must be raised in order to produce this number. For instance, logarithm of 100 with base 10 would be 2 i.e. log100=2 since 10 raised in the power of "2" produces 100. Antilogarithm is an inverse operation that finds the number given the logarithm value (power) and base.

Things You'll Need

• Calculator

Instructions

1. Determine the logarithm base. Note: the base is typically not given for the two most widely used logarithms. It should be determined from the logarithm notation.
   The symbols "log" or "lg" indicate logarithm with base 10. The symbol "ln" or loge" denote the natural logarithm with the base equals to the mathematical constant "e". The value of "e" (rounded to the fifth digit) is 2.71828.
   For all other logarithms the base should to be explicitly defined. For instance, log2(67) has the base "2."

2. Raise base in the power of logarithm value to calculate antilogarithm.
   Antilogarithm= base^(value).
   For example, calculate antilogarithm if log=-3. "Log" means that the base is 10 (Step 1). Antilogarithm=10^(-3)=0.001.

3. Calculate antilogarithm using the calculator. Enter the base magnitude, then press the button "x^y" (or "y^x") and enter logarithm value. Press the "=" button.
   For example, if log3=6.9345 is given, then antilogarithm is 2035.1543 (rounded).

4. Calculate antilogarithm if logarithm given as logx(Y) e.g. log6(784). In such case you need neither to calculate logarithm value nor raise the base in the power. Instead get an instant answer: Antilogarithm=Y. In our example, antilogarithm of log6(784) is 784.

References

• "Algebra II (Cliffs Quick Review)", E. Kohn and D.A. Herzog, May 29, 2001.