log2

Compute the base-2 logarithm of a numeric input.

y = log2(4^(1/3))

y = 
0.6667

Compute the base-2 logarithm of a symbolic input. The result is in terms of the natural logarithm log function.

syms x
ySym = log2(x^(1/3))

ySym = 
$$\frac{\log \left(x^{1/3}\right)}{\log \left(2\right)}$$

Substitute the symbolic variable x with a number by using subs. Simplify the result by using simplify.

yVal = subs(ySym,x,4)

yVal = 
$$\frac{\log \left(4^{1/3}\right)}{\log \left(2\right)}$$

simplify(yVal)

ans = 
$$\frac{2}{3}$$

Find the mantissa and exponent of a base-2 logarithm of an input $$X$$. The mantissa $$F$$ and the exponent $$E$$ satisfy the relation $$X=F\cdot 2^E$$.

Create a symbolic variable a and assume that it is real. Create a symbolic vector X that contains symbolic numbers and expressions. Find the exponent and mantissa for each element of X.

syms a real;
X = [1 0.5*2^a 5/7]

X = 
$$\left(\begin{array}{ccc}1& \frac{2^a}{2}& \frac{5}{7}\end{array}\right)$$

[F,E] = log2(X)

F = 
$$\left(\begin{array}{ccc}\frac{1}{2}& \frac{\frac{1}{2^{\lfloor \frac{\log \left(\frac{2^a}{2}\right)}{\log \left(2\right)}\rfloor +1}}\hspace{0.17em}{2}^a}{2}& \frac{5}{7}\end{array}\right)$$

E = 
$$\left(\begin{array}{ccc}1& \lfloor \frac{\log \left(\frac{2^a}{2}\right)}{\log \left(2\right)}\rfloor +1& 0\end{array}\right)$$

The values returned in F have magnitudes in the range 0.5 <= abs(F) < 1.

Simplify the results using simplify.

F = simplify(F)

F = 
$$\left(\begin{array}{ccc}\frac{1}{2}& 2^{a-\lfloor a\rfloor -1}& \frac{5}{7}\end{array}\right)$$

E = simplify(E)

E = $$\left(\begin{array}{ccc}1& \lfloor a\rfloor & 0\end{array}\right)$$