log 2*$10^{8}$ + log 3*$10^{5}$

asked by guest
on Sep 20, 2024 at 5:22 pm



You asked:

Evaluate the expression: \(\log\left( 2 \right) \cdot {10}^{8} + \log\left( 3 \right) \cdot {10}^{5}\)

MathBot Answer:

\[\log\left( 2 \right) \cdot {10}^{8} + \log\left( 3 \right) \cdot {10}^{5} = 100000 \log{\left(3 \right)} + 100000000 \log{\left(2 \right)} \approx 69424579.28486134191086273666950990937801\]

\[\begin{aligned}\log\left( 2 \right) \cdot {10}^{8} + \log\left( 3 \right) \cdot {10}^{5}& = \log{\left(2 \right)} \cdot 10^{8} + \log{\left(3 \right)} \cdot 10^{5}\\& = \log{\left(2 \right)} \cdot 100000000 + \log{\left(3 \right)} \cdot 10^{5}\\& = 100000000 \cdot \log{\left(2 \right)} + \log{\left(3 \right)} \cdot 10^{5}\\& = 100000000 \cdot \log{\left(2 \right)} + \log{\left(3 \right)} \cdot 100000\\& = 100000000 \cdot \log{\left(2 \right)} + 100000 \cdot \log{\left(3 \right)}\\& = 100000 \cdot \log{\left(3 \right)} + 100000000 \cdot \log{\left(2 \right)}\end{aligned}\]

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