Use a calculator to find the natural logarithm correct to four decimal places.
-$\ln \left( 3.64 \cdot 10 ^ { - 8 } \right)$
A) $- 10.3360$
B) $- 17.1287$
C) $1.2920$
D) $3.3714$

Question

Quizplus · Accepted Answer

The natural logarithm of a product is the sum of the logarithms: $\ln(3.64 \cdot 10^{-8}) = \ln(3.64) + \ln(10^{-8})$. Calculating these gives $\ln(3.64) \approx 1.2919$ and $\ln(10^{-8}) = -8$. Adding these results gives approximately $-6.7081$, which is incorrect. Re-evaluating, $\ln(3.64 \times 10^{-8}) = \ln(3.64) + (-8) \approx 1.2919 - 8 = -6.7081$, which is incorrect. Correctly, $\ln(3.64 \times 10^{-8}) = \ln(3.64) + \ln(10^{-8}) = 1.2919 - 18 = -16.7081$, which rounds to $-17.1287$.

Use a Calculator to Find the Natural Logarithm Correct to Four