How to Calculate Log2

Logarithm of a number is the power to which the base must be raised in order to produce this number. Logarithm with base 10 is called a common logarithm and denoted as "log." For example, log1000 would be 3, as 10 raised in the power of 3 produces 1000. Every scientific calculator has a built-in function to calculator log of any number (typically the button "log"). But none can calculate log2, which is logarithm with base 2, directly. As an example, calculate log2 of the number "12" i.e. log2(12).

Things You'll Need

• Any calculator having "log" function.

Instructions

1. Express log2(Y) of any number Y via logY. According to the logarithm definition Y=2^(log2(Y)). Take log of both sides of the equation to get
   logY=log(2^(log2(Y))=log2(Y) x log2. Then divide both sides by "log2" to get
   Log2(Y)=log(Y)/log2.

2. Calculate log2 with a calculator. Enter "2" and press the "log" button.
   log2=0.30103. Write down this constant as it will be used in all calculations of log2.

3. Calculate logY . Enter a number and press the "log" button.
   In our example, log12= 1.07918.

4. Divide the result from Step 3 by the constant obtained in Step 2 to get log2(Y).
   In our example, it would be log2(12)=log12/log2=1.07918/0.30103=3.584958.

References

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