Using numerical analysis and the Power Rule of Logarithms, log x^k=k log x

Question

, how can log(1/100)
be rewritten?(1 point)
Responses

−2log10
negative 2 logarithm 10

2log−10
2 logarithm negative 10

10log−2
10 logarithm negative 2

log−20

Answer 1

To rewrite \( \log(1/100) \) using the Power Rule of Logarithms, we can follow these steps:

1. Recognize that \( \frac{1}{100} \) can be expressed as \( 100^{-1} \).
2. Apply the log property: \( \log(a/b) = \log a - \log b \).
3. Thus, we have: \[ \log(1/100) = \log(100^{-1}) = -1 \cdot \log(100). \]
4. Since \( 100 = 10^2 \), we can further write: \[ \log(100) = \log(10^2) = 2 \log(10). \]

Combining these, we get: \[ \log(1/100) = -1 \cdot 2 \log(10) = -2 \log(10). \]

So, the correct numerical analysis is:

−2log10 (negative 2 logarithm 10).