log(x+(3/10))+logx+1=0
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To solve the equation log(x + (3/10)) + log(x) + 1 = 0, we can use logarithmic properties and algebraic manipulation. Here's the step-by-step solution:
1. Start by combining the logarithmic terms. According to the logarithmic property log(a) + log(b) = log(ab), we can rewrite the equation as:
log(x + (3/10)) + log(x) = -1
2. Apply another logarithmic property log(b) = c can be rewritten as b = 10^c. In this case, we have:
(x + (3/10)) * x = 10^(-1)
3. Simplify the right side of the equation:
(x + (3/10)) * x = 1/10
4. Expand the left side of the equation:
x^2 + (3/10)x = 1/10
5. Multiply the entire equation by 10 to eliminate the fractions:
10x^2 + 3x = 1
6. Rearrange the equation in standard quadratic form:
10x^2 + 3x - 1 = 0
Now, you can solve this quadratic equation using various methods, such as factoring, completing the square, or using the quadratic formula.