Problema Solution
Use the Distance Modulus Formula, M=5logr−5(where Mis the distance modulus and ris the distance from Earth to a star in parsecs), and the fact that 1parsec is approximately 3.3light years, to find the distance in light years from Earth to a star with distance modulus 0.67.
Answer provided by our tutors
The wording of the problem statement is difficult to interpret for a variety of reasons. I assume that "Mis" is "M is", "ris" is "r is", "1parsec" is "1 parsec" so that "parsec" is something like a unit. Knowing, however, how to interpret "5logr−5" is a bigger issue because it could either be "5log(r-5)" or "5log(r)-5"... or other possibilities.
We assume that "log" is a 10-base log, that 3.3 light years is the unit in "parsecs"...
based on those assumptions, solve for 'r' in parsec units:
0.67 = 5*log(r)-5
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r=13.61
to convert from parsec to light years:
13.61 * 3.3 = 44.91
so converting 'r' to light years the distance in light years is approximately 45 light years