How can I obtain the most simplified version of the symbolic solution of an equation that contains such functions as 'log' in a fractional and not decimal representation?

Given is an equation that is sought to be symbolically solved in MATLAB using the Symbolic Math Toolbox, namely,

syms x
eqn = log(2*x)/log(3)==-1

It is known that the analytical solution of the latter equation is the following one,

res =
 
1/6

However, when using the function 'solve' from MATLAB and then the command 'simplify' with the Name-Value pair 'IgnoreAnalyticConstraints'-true, then 'log(3)' is firstly replaced by the fractional number '2473854946935173/2251799813685248' and as a result, the resulting expression appears still complex, namely,

>> res = simplify(solve(eqn,x,'IgnoreAnalyticConstraints',true))

res = 

exp(-2473854946935173/2251799813685248)/2

MATLAB cannot simplify this expression further to '1/6' which is the expected solution.

How can I obtain the most simplified version of the symbolic solution of an equation that contains such functions as 'log' in a fractional and not decimal representation?

Answer 1

[MathWorks Support Team]

In this case one needs to prevent MATLAB from expanding expression 'log(3)' to the aforementioned fractional number. To achieve this, please use an additional symbolic variable in the place of number 3, say 'y', solve the equation symbolically and substitute 'y' with 3 in the solution, namely,

syms x y
eqn = log(2*x)/log(y) == -1;
res = simplify(solve(eqn,x,'IgnoreAnalyticConstraints',true));
res = subs(res, y, 3);

This way the desirable result '1/6' can be obtained.

Another workaround is to declare the number 3 within function 'log' as symbolic, in which case the expression log(3) won't be expanded by MATLAB, see the following lines of code,

syms x
eqn = log(2*x)/log(sym(3))==-1
simplify(solve(eqn,x,'IgnoreAnalyticConstraints',true))