Question

I have an ACT practice problem that I need help onPlease answer these questions as well, *Where did Arjun make errors?**Explain the errors he made and the properties of logarithms that leads to the correct answer, state the correct answer*

Answer 1

The given logarithmic expression is:

`\log _7x+\log _7y-\log _7z`

The error made was that the x was added to y and then z was subtracted, instead of multiplying and dividing, respectively.

Recall the Quotient and Product Properties of Logarithm:

`\begin{gathered} \log _bm+\log _bn=\log _b(mn) \\ \log _bm-\log _bn=\log _b((m)/(n)) \end{gathered}`

Applying this to the given expression:

`\log _7x+\log _7y-\log _7z=\log _7(xy)-\log _7z=\log _7((xy)/(z))`

The error made was that x was added to y and then z was subtracted, instead of multiplying and dividing, respectively.

The properties of logarithms that lead to the correct answer are the Quotient and Product Properties of Logarithm.

The correct answer is:

`\log _7x+\log _7y-\log _7z=\log _7((xy)/(z))`