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Fungrim entry: 77aa12

log ⁣(x+a)log(x)log ⁣(1+axa)\left|\log\!\left(x + a\right) - \log(x)\right| \le \log\!\left(1 + \frac{\left|a\right|}{x - \left|a\right|}\right)
Assumptions:xR  and  aR  and  a0  and  a<xx \in \mathbb{R} \;\mathbin{\operatorname{and}}\; a \in \mathbb{R} \;\mathbin{\operatorname{and}}\; a \ge 0 \;\mathbin{\operatorname{and}}\; \left|a\right| < x
\left|\log\!\left(x + a\right) - \log(x)\right| \le \log\!\left(1 + \frac{\left|a\right|}{x - \left|a\right|}\right)

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; a \in \mathbb{R} \;\mathbin{\operatorname{and}}\; a \ge 0 \;\mathbin{\operatorname{and}}\; \left|a\right| < x
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
Loglog(z)\log(z) Natural logarithm
RRR\mathbb{R} Real numbers
Source code for this entry:
    Formula(LessEqual(Abs(Sub(Log(Add(x, a)), Log(x))), Log(Add(1, Div(Abs(a), Sub(x, Abs(a))))))),
    Variables(x, a),
    Assumptions(And(Element(x, RR), Element(a, RR), GreaterEqual(a, 0), Less(Abs(a), x))))

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2021-03-15 19:12:00.328586 UTC