Question

Propose an equation similar to log 4 + log x = log 27 whose solution is 9+

Answer 1

To propose the equation we first need to remember that:

`\log (a)+\log (b)=\log (ab)`

Let's solve the equation given to help us:

`\begin{gathered} \log 4+\log x=\log 27 \\ \log 4x=\log 27 \end{gathered}`

since we have the same logarithm in both sides of the equations this means that their arguments have to be equal then we have that:

`\begin{gathered} 4x=27 \\ x=(27)/(4) \end{gathered}`

From the solution of the equation given we notice that if the number 4 were a 3 instead we will have 9 as a solution (since 27 divided by 3 is 9).

Therefore we can propose the equation:

`\log 3+\log x=\log 27`

Just to verify the solution is nine like we want let's solve the equation:

`\begin{gathered} \log 3+\log x=\log 27 \\ \log 3x=\log 27 \\ 3x=27 \\ x=(27)/(3) \\ x=9 \end{gathered}`

hence the solution is nine and the equation we proposed fullfils what the problem ask for.