Respuesta :
The order of the steps to solve the provided logarithmic equation is arranged as,
[tex](x^2 - 15) =(2x)[/tex]
[tex]x^2 +2x-15=0[/tex]
[tex](x-5)(x+3)=0[/tex]
[tex]x-5=0,x+3=0[/tex]
Potential solution are -3 and 5.
What is exponent of log rule?
The exponent of the log rule says that the raising a logarithm with a number to its base is equal to the number.
When the base is common ion equality equation, then the two log values can be compares using exponent rule of logarithm.
The given logarithmic equation in the problem is,
[tex]\log(x^2 - 15) = \log(2x)[/tex]
The order of solution of the above expression,
- Step 1,
As the base is common, then the two log values can be compares using exponent rule of logarithm.
[tex](x^2 - 15) =(2x)[/tex]
- Step 2,
Bring all the terms, one side of the expression as,
[tex]x^2 +2x-15=0[/tex]
- Step 3,
Find the factors of the above quadratic equation using the split the middle term method as,
[tex]x^2 -5x+3x-15=0\\x(x-5)+3(x-5)=0\\(x-5)(x+3)=0[/tex]
- Step 4,
Equate the factors to the zero to find out the values of x,
[tex]x-5=0,x+3=0[/tex]
- Step 5,
The potential solution are,
[tex]x=5,-3[/tex]
Thus, the order of the steps to solve the provided logarithmic equation is arranged as,
[tex](x^2 - 15) =(2x)[/tex]
[tex]x^2 +2x-15=0[/tex]
[tex](x-5)(x+3)=0[/tex]
[tex]x-5=0,x+3=0[/tex]
Potential solution are -3 and 5.
Learn more about the rules of logarithmic function here;
https://brainly.com/question/13473114
