Question

Using numerical analysis and the Power Rule of Logarithms, logxk=klogx , how can log(1/100) be rewritten?(

Answer 1

To rewrite \( \log(1/100) \) using the Power Rule of Logarithms, we can start by expressing \( 1/100 \) as \( 100^{-1} \). This way, we can apply the logarithmic properties.

1. Rewrite \( \log(1/100) \):
\[
\log(1/100) = \log(100^{-1})
\]

2. Apply the Power Rule of Logarithms:
\[
\log(100^{-1}) = -1 \cdot \log(100)
\]

3. We know that \( 100 = 10^2 \), so we can further simplify \( \log(100) \):
\[
\log(100) = \log(10^2) = 2 \log(10)
\]

4. Substituting this back into our expression:
\[
-1 \cdot \log(100) = -1 \cdot 2 \log(10) = -2 \log(10)
\]

Thus, we can write the expression \( \log(1/100) \) as:
\[
\log(1/100) = -2 \log(10)
\]

If the logarithm is base 10, this can be approximated as:
\[
\log(1/100) = -2
\]

So, the final rewritten form is:
\[
\log(1/100) = -2 \log(10)
\]
or simply \( -2 \), if the base is 10.