Question

I need help with log question. ​

Answer 1

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

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)}`