Answer:
The equation has the solution(s) x = - 5, and x = 2
Step-by-step explanation:
Let's start by adding log(10) to either side of the equation --- (1)
[tex]\log _{10}\left(x^2+3x\right)-\log _{10}\left(10\right)+\log _{10}\left(10\right)=0+\log _{10}\left(10\right)[/tex]
= [tex]\log _{10}\left(x^2+3x\right)=\log _{10}\left(10\right)[/tex]
If you recall, one property proves that [tex]\log _{10}\left(10\right):\qu 1[/tex]. We can substitute this value back into the simplified equation --- (2)
[tex]\log _{10}\left(x^2+3x\right)=1[/tex]
We can also apply the logarithmic definition, If logₐ(b) = c then b = aᶜ. Using this definition we receive a further simplified equation --- (3)
[tex]x^2+3x=10^1[/tex]
[tex]x^2+3x=10[/tex]
Solving for the expression we receive the solution(s) x = 2, and x = - 5, our first option.
Note : The first solution is correct, but I wanted to take a slightly different approach
