log(3.162*10^-5)
You asked:
Evaluate the expression: \(\log\left( 3.162 \cdot {10}^{-5} \right)\)
MathBot Answer:
\[\log\left( 3.162 \cdot {10}^{-5} \right) = \log{\left(\frac{1581}{50000000} \right)} \approx -10.36172072618294814515275533667873\]
\[\begin{aligned}\log\left( 3.162 \cdot {10}^{-5} \right)& = \log{\left(\left(3 + \frac{162}{1000}\right) \cdot \frac{1}{10^{5}} \right)}\\& = \log{\left(\left(3 + \frac{81}{500}\right) \cdot \frac{1}{10^{5}} \right)}\\& = \log{\left(\frac{1581}{500} \cdot \frac{1}{10^{5}} \right)}\\& = \log{\left(\frac{1581}{500} \cdot \frac{1}{100000} \right)}\\& = \log{\left(\frac{1581}{50000000} \right)}\end{aligned}\]