Evaluate - log of 2*10^-2

$- \log (2) \cdot 10^{- 2}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- \log (2) \cdot \frac{1}{10^{2}}$

Raise $10$ to the power of $2$ .

$- \log (2) \cdot \frac{1}{100}$

Simplify $\frac{1}{100} \log (2)$ by moving $\frac{1}{100}$ inside the logarithm.

$- \log (2^{\frac{1}{100}})$

The result can be shown in multiple forms.

Exact Form:

$- \log (2^{\frac{1}{100}})$

Decimal Form:

$- 0.00301029 \dots$