We cal solve the equation using logarithms properties:
[tex]\log_6x+\log_63=\log_6(x+1)[/tex]
Use the next logarithm rule:
[tex]\log_bM+\log_bN=\log_bMN[/tex]
Then,
[tex]\log_6x+\log_63=\log_63x[/tex]
Hence, we have the next equation:
[tex]\log_63x=\log_6(x+1)[/tex]
Now, use the equality property:
[tex]\begin{gathered} if\text{ }\log_bm=\log_bn \\ Then \\ m=n \end{gathered}[/tex]
Hence,
[tex]\begin{gathered} 3x=x+1 \\ \end{gathered}[/tex]
Solve for:
[tex]\begin{gathered} 3x-x=1 \\ 2x=1 \\ x=\frac{1}{2} \end{gathered}[/tex]
Hence, the correct answer is 1/2.
The answer is option x= 1/2.
