m=2-x/hc, where m is the mass.
We know that h=5730 years when m=½c (definition of half-life), so let's see if the formula works when x=5730 years:
½c=2-1c, ½=1/2✔️
If the mummy has lost 57% of its C14 then its mass m=0.43c.
From the formula: 0.43c=2-x/5730c.
2-x/5730=0.43,
(-x/5730)log(2)=log(0.43),
x=-5730log(0.43)/log(2)=6976.8 years, rounded to the nearest year is 6,977 years, so the mummy is about 6,977 years old.