What is ln|40|-ln|40-10000| ?

The solution to ln|40|-ln|40-10000| is -ln(249)

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simplify ln|40|-ln|40-10000|

simplify

ln ∣ 40 ∣ - ln ∣ 40 - 10000 ∣

- ln (249)

Decimal Notation

- 5.51745 \dots

Solution steps

ln ∣ 40 ∣ - ln ∣ 40 - 10000 ∣

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln ∣ 40 ∣ - ln ∣ 40 - 10000 ∣ = ln (\frac{∣ 40 ∣}{∣ 40 - 10000 ∣})

= ln (\frac{∣ 40 ∣}{∣ 40 - 10000 ∣})

\frac{∣ 40 ∣}{∣ 40 - 10000 ∣} = \frac{1}{249}

= ln (\frac{1}{249})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (249)

lo g_{10} (x^{3} y^{2})

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\frac{1}{2} ln ∣ x + 1 ∣ + \frac{3}{2} ln ∣ x - 1 ∣

lo g_{10} ((\frac{x ^{4}}{( x ^{2} + 1 ) ^{\frac{1}{3}}}) (x - 1)^{2})

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