Respuesta :
The value which shows the true solution to the logarithmic equation solved below is 1.
What is domain and range of function?
Domain of a function is the set of all the possible input values which are valid for that function.
Range of a function is the set of all the possible output values which are valid for that function.
The given logarithmic equation is,
[tex]\log_2x+\log_2(x+7)=3[/tex]
Use the addition property of log in above expression.
[tex]\log_2[x\times(x+7)]=3[/tex]
Use the power rule property of log in above expression.
[tex][x\times(x+7)]=2^3\\x\times(x+7)=8\\x^2+7x-8=0[/tex]
Solve the quadratic equation with the help of split the middle term method,
[tex]x^2+8x-1x-8=0\\x(x+8)-1(x+8)=0\\(x+8)(x-1)=0\\x=-8,1[/tex]
Here, the two values of variable we get. One is positive and another is negative. As the logarithmic function is defined only for positive real number as its input.
Thus, the value which shows the true solution to the logarithmic equation solved above is 1.
Learn more about the domain and range of the function here;
https://brainly.com/question/2264373
