log 100 - 2 log 0.001

asked by guest
on Nov 18, 2024 at 6:51 am



You asked:

Evaluate the expression: \(\log\left( 100 \right) - 2 \cdot \log\left( 0.001 \right)\)

MathBot Answer:

\[\log\left( 100 \right) - 2 \cdot \log\left( 0.001 \right) = \log{\left(100 \right)} + 2 \log{\left(1000 \right)} \approx 18.42068074395236547214393163747491\]

\[\begin{aligned}\log\left( 100 \right) - 2 \cdot \log\left( 0.001 \right)& = \log{\left(100 \right)} - 2 \cdot \log{\left(\frac{1}{1000} \right)}\\& = \log{\left(100 \right)} - 2 \cdot - \log{\left(1000 \right)}\\& = \log{\left(100 \right)} - -2 \cdot \log{\left(1000 \right)}\\& = \log{\left(100 \right)} + 2 \cdot \log{\left(1000 \right)}\\& = 2 \cdot \log{\left(1000 \right)} + \log{\left(100 \right)}\end{aligned}\]

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