Solve the following system of equations in positive real numbers (the logarithm is in base 10):
Let . Then the equations become
The first two equations can be written and , from which it follows that and so . Substitute that into the third equation, and you find that , from which it follows that and .
So , or , from which , . The expressions for y and z are similar but more awkward, because they will involve raising numbers to irrational powers.