log₂( x ) is easily calculated even in ASM, as follows.
Then, calculate
log₁₀( x )
    = log₂( x ) / log₂( 10 )
    = log₂( x ) * log₁₀( 2 )
where log₁₀( 2 ) = 0.30103

As of calculation of log₂( x ), I'll show an example of the calculation of a 16-bit integer number, 1ABCH here.

First, represent the number in binary and find the left-most '1'.

1ABCH   0001 1010 1011 1100

The position (digit) of '1' is 12, where the right-most position is zero.
This number equals to the integer part of log₂( x )

1000H   0001 0000 0000 0000   212
1ABCH   0001 1010 1011 1100
2000H   0010 0000 0000 0000   213

212 <     1ABCH     < 213
12  < log2( 1ABCH ) < 13

This number is also obtained by left shit until the carry gives '1'
Four times of left shit provides the carry of '1', in this case.

carry
      0001 1010 1011 1100  - 1ABCH
    0 0011 0101 0111 1000  - left-shift once
    0 0110 1010 1111 0000  - left-shift twice
    0 1101 0101 1110 0000  - left-shift third
    1 1010 1011 1100 0000  - left-shift fourth

Then, the position is calculated by subtracting the shift number from the number of total bits.
16 - 4 = 12


Now, calculate the decimal part of log₂( x )
Assume decimal point after the carry of above result.

    1.1010 1011 1100 0000
     ^
   decimal point

This fixed point number equals to 1ABCH / 2¹²
1ABCH * 2⁴ / 2¹⁶ = 1ABCH / 2¹²

Also, log₂ of this number gives the decimal part of log₂( x )
log₂( 1ABCH / 2¹² ) = log₂( 1ABCH ) - 12

This number always falls between 1 and 2, regardless of the original number.

212 <    1ABCH    < 213
1   < 1ABCH / 212 < 2

Then, using look-up table, log₂ of this number is obtained.
To apply look-up table, we don't need to use all digits of this number.
1) The first digit is always 1
2) Depending on the required precision, take the limited number of greater digits.

For example, the first eight digits of decimal part is applied to the look-up table.
1.1010 1011 1100 0000

The look-up table is given as
y = log₂(x + 1) (0 <= x < 1)

Adding the above integer part and the result of look-up table (decimal part), the entire fixed point number of log₂( x ) is obtained.

In this way, log₁₀( x ) calculation is reduced to fixed point math using ASM.

Tsuneo