Question

Using numerical analysis and the Power Rule of Logarithms, logxk=klogx
, how can log(1100)
be rewritten?

Answer 1

To rewrite \( \log(1100) \) using the Power Rule of Logarithms, we first need to express \( 1100 \) as a product of its factors. One way to do this is:

\[
1100 = 11 \times 100
\]
We can further break down \( 100 \) as \( 10^2 \):

\[
1100 = 11 \times 10^2
\]

Now, we can apply the logarithmic identity that states \( \log(a \times b) = \log(a) + \log(b) \) to rewrite \( \log(1100) \):

\[
\log(1100) = \log(11 \times 10^2) = \log(11) + \log(10^2)
\]

Now, applying the Power Rule of Logarithms \( \log(x^k) = k \cdot \log(x) \):

\[
\log(10^2) = 2 \cdot \log(10)
\]

Thus, we have:

\[
\log(1100) = \log(11) + 2 \cdot \log(10)
\]

You can further simplify this if you know the value of \( \log(10) \), which is equal to 1 in base 10 logarithms. Therefore:

\[
\log(1100) = \log(11) + 2
\]

In conclusion, the expression for \( \log(1100) \) can be rewritten as:

\[
\log(1100) = \log(11) + 2
\]