Respuesta :
The solution of the logarithmic equation provided using the log rule is,
[tex]x=-3[/tex]
What is the log rule for same base?
When the base of the logarithm in an equality expression is same, then the number are directly compared to each other.
The given logarithmic equation in the problem is,
[tex]\log_7(x -4) = \log_7(4x +5)\\[/tex]
Compare the number for the same base as,
[tex](x-4)=(4x+5)[/tex]
Solve the equation further as,
[tex]4x-x=-4-5\\3x=-9\\x=\dfrac{-9}{3}\\x=-3[/tex]
Thus, the solution of the logarithmic equation provided using the log rule is,
[tex]x=-3[/tex]
Learn more about the rules of logarithmic function here;
https://brainly.com/question/13473114
