The potential solutions of logarithmic function using the logarithmic properties are found as -9 and 4.
The product of the log rule says that the sum of number of logarithm functions is equal to the log function of product of all the numbers, given that base is same.
The given logarithmic function in the problem is,
[tex]\log_6x+\log(6x+5)=2[/tex]
Using the product rule of logarithmic function, the above equation can be written as,
[tex]\log_6(x\times(x+5))=2\\\log_6(x^2+5x))=2[/tex]
Using the equality rule of logarithmic function, the above equation can be written as,
[tex]x^2+5x=6^2\\x^2+5x=36[/tex]
Take all the terms one side of the equation as,
[tex]x^2+5x-36=0[/tex]
Find the factors of above equation using the split the middle term method as,
[tex]x^2+9x-4x-36=0\\x(x+9)-4(x+9)=0\\(x+9)(x-4)=0[/tex]
By equating these factor to the zero one by one, we get the potential solution as -9 and 4.
Thus, the potential solutions of logarithmic function using the logarithmic properties are found as -9 and 4.
Learn more about the rules of logarithmic function here;
https://brainly.com/question/13473114
Answer:
-9 and 4
Step-by-step explanation:
Did it on edge :)
