Simplify - log\(_{10}\) 0.00001.

Answer Details

Logarithms help us answer the question: "To what power must we raise a certain base to get a particular number?" In this case, we are working with base 10 logarithms (log\(_{10}\)). The expression given is \(- \log_{10} 0.00001\).

First, recall the definition:

• \(\log_{10} x\) is the power to which 10 must be raised to get \(x\).

Let's break it down:

• What is \(0.00001\) in terms of powers of 10? We can write \(0.00001\) as \(10^{-5}\), because:

\[ 10^{-5} = \frac{1}{10^5} = 0.00001 \]

Now use the property of logarithms that says \(\log_{10}(10^a) = a\):

\[ \log_{10}(0.00001) = \log_{10}(10^{-5}) = -5 \]

But the original question asks for the negative of this value:

\[ - \log_{10}(0.00001) = -(-5) = 5 \]

Therefore, the simplified value is \(5\).

• This is because the logarithm gives the exponent: \(10^{-5} = 0.00001\), so the log is \(-5\). The negative sign outside gives us \(5\).