DLMF:4.5.E5 (Q1558)

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DLMF:4.5.E5
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    Statements

    Defining formula
    ln ⁡ x ≤ a ⁢ ( x 1 / a - 1 ) , 𝑥 𝑎 superscript 𝑥 1 𝑎 1 {\displaystyle{\displaystyle\ln x\leq a(x^{1/a}-1),}}
    0 references
    DLMF id
    DLMF:4.5.E5
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    constraint
    x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}
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    Symbols used
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2addec
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    Q11221
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C4.S1.XMD4.m1dec
    0 references
    Q11218
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1ddec
    0 references
     
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