The solution to the given logarithmic function is; x = ¹/₅ and -¹/₂
We want to solve;
log (x+3/10) + log (x) + 1 = 0
Subtracting 1 from both sides, we have;
log (x+3/10) + log (x) = -1
From properties of logarithms, we know that;
log₂a + log₂b = log₂(a*b)
Thus;
log (x+3/10) + log (x) = -1 can be expressed as;
log (x(x + 3)/10) = -1
Also, from properties of logarithms;
log₂a = 3 is also a = 2³
Thus;
log (x(x + 3)/10) = -1 is;
(x(x + 3)/10) = 10⁻¹
x² + ³/₁₀x = 1/10
Multiply through by 10 to get;
10x² + 3x = 1
⇒ 10x² + 3x - 1 = 0
Using online quadratic equation calculator, we have;
x = ¹/₅ and -¹/₂
Read more about properties of logarithms at; https://brainly.com/question/450777
