Question

I have an ACT practice problem that I’m having trouble on

Answer 1

Given below the logarithm terms

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

In order to resolve the above problem, we will apply two properties of the logarithm.

These properties are,

`\begin{gathered} \log _c\mleft(a\mright)+\log _c\mleft(b\mright)=\log _c\mleft(ab\mright)\ldots\ldots.1 \\ \quad \log _c\mleft(a\mright)-\log _c\mleft(b\mright)=\log _c\mleft((a)/(b)\mright)\ldots\ldots.2 \end{gathered}`

Hence,

`\begin{gathered} \log _7x+\log _7y-\log _7z=\log _7(\mleft(x* y\mright))/(z) \\ \log _7x+\log _7y-\log _7z=\log _7\mleft((xy)/(z)\mright) \end{gathered}`

Therefore,

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

The error he did was that instead of multiplying, he added, and also instead of dividing he subtracted.

The correct answer is,

`\log _7((xy)/(z))`