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Sagot :
To propose the equation we first need to remember that:
[tex]\log (a)+\log (b)=\log (ab)[/tex]Let's solve the equation given to help us:
[tex]\begin{gathered} \log 4+\log x=\log 27 \\ \log 4x=\log 27 \end{gathered}[/tex]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:
[tex]\begin{gathered} 4x=27 \\ x=\frac{27}{4} \end{gathered}[/tex]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:
[tex]\log 3+\log x=\log 27[/tex]Just to verify the solution is nine like we want let's solve the equation:
[tex]\begin{gathered} \log 3+\log x=\log 27 \\ \log 3x=\log 27 \\ 3x=27 \\ x=\frac{27}{3} \\ x=9 \end{gathered}[/tex]hence the solution is nine and the equation we proposed fullfils what the problem ask for.
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