Question

I need help with log question. ​

Answer 1

Answer:

Ramona's answer is correct, Fiona's contains a mistake.

Step-by-step explanation:

We begin with the equation $3x=2\log{(1000)}$. 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:

$\log{(a^n)}=n\log{(a)}$

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

$3x=2\log{(1000)}\\3x=(\log{(1000)})^2$

When it should read (as Ramona's does):

$3x=2\log{(1000)}\\3x=\log{(1000^2)}$