Questions: Simplify the expression without using a calculator. log 0.00000001=

Solution Steps

The expression given is \(\log 0.00000001\). We need to simplify this logarithmic expression.

The number \(0.00000001\) can be written in scientific notation as \(1 \times 10^{-8}\).

Using the property of logarithms that states \(\log(a \times b) = \log a + \log b\), we can rewrite the expression:

\[ \log(1 \times 10^{-8}) = \log 1 + \log 10^{-8} \]

Since \(\log 1 = 0\), the expression simplifies to:

\[ 0 + \log 10^{-8} = \log 10^{-8} \]

Using the property \(\log 10^b = b\), we have:

\[ \log 10^{-8} = -8 \]

Final Answer