2log(6) + log(81) - log(27) - log(12) =

asked by guest
on Oct 04, 2024 at 11:45 pm



You asked:

Evaluate the expression: \(2 \cdot \log\left( 6 \right) + \log\left( 81 \right) - \log\left( 27 \right) - \log\left( 12 \right)\)

MathBot Answer:

\[2 \cdot \log\left( 6 \right) + \log\left( 81 \right) - \log\left( 27 \right) - \log\left( 12 \right) = - \log{\left(27 \right)} - \log{\left(12 \right)} + 2 \log{\left(6 \right)} + \log{\left(81 \right)} \approx 2.19722457733621938279049047384505\]

\[\begin{aligned}2 \cdot \log\left( 6 \right) + \log\left( 81 \right) - \log\left( 27 \right) - \log\left( 12 \right)& = 2 \cdot \log{\left(6 \right)} + \log{\left(81 \right)} - \log{\left(27 \right)} - \log{\left(12 \right)}\\& = \left(2 \cdot \log{\left(6 \right)} + \log{\left(81 \right)}\right) - \log{\left(27 \right)} - \log{\left(12 \right)}\\& = \left(- \log{\left(27 \right)} + 2 \cdot \log{\left(6 \right)} + \log{\left(81 \right)}\right) - \log{\left(12 \right)}\\& = - \log{\left(12 \right)} - \log{\left(27 \right)} + 2 \cdot \log{\left(6 \right)} + \log{\left(81 \right)}\end{aligned}\]

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