Answer:
Ramona's answer is correct, Fiona's contains a mistake.
Step-by-step explanation:
We begin with the equation [tex]3x=2\log{(1000)}[/tex]. Both try to use the exponent law of logarithms, but Fiona makes a mistake in where she puts the exponent. In case you've forgotten, this law says that, given a number a and an exponent n:
[tex]\log{(a^n)}=n\log{(a)}[/tex]
Fiona's mistake was in putting the exponent above the whole logarithm, instead of inside the argument (the number inside the parentheses). Fiona's step reads
[tex]3x=2\log{(1000)}\\3x=(\log{(1000)})^2[/tex]
When it should read (as Ramona's does):
[tex]3x=2\log{(1000)}\\3x=\log{(1000^2)}[/tex]
