ln(40)-ln(40-1000)

asked by guest
on Oct 23, 2024 at 11:26 am



You asked:

Evaluate the expression: \(\ln\left( 40 \right) - \ln\left( 40 - 1000 \right)\)

MathBot Answer:

\[\ln\left( 40 \right) - \ln\left( 40 - 1000 \right) = - \log{\left(960 \right)} + \log{\left(40 \right)} - i \pi\]

\[\begin{aligned}\ln\left( 40 \right) - \ln\left( 40 - 1000 \right)& = \log{\left(40 \right)} - \log{\left(40 - 1000 \right)}\\& = \log{\left(40 \right)} - \log{\left(-960 \right)}\\& = \log{\left(40 \right)} - \left(\pi \cdot i + \log{\left(960 \right)}\right)\\& = - \log{\left(960 \right)} - \pi \cdot i + \log{\left(40 \right)}\end{aligned}\]

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