Questions: Find the exact value. [ log 10^5 ]

Find the exact value. [ log 10^5 ]
Transcript text: Find the exact value. \[ \log 10^{5} \]
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Solution

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Solution Steps

Step 1: Evaluate the Expression

We start with the expression \( \log 10^{5} \). According to the properties of logarithms, we can simplify this expression using the identity:

\[ \log_{10}(10^{x}) = x \]

Step 2: Apply the Identity

In our case, we have \( x = 5 \). Therefore, we can directly apply the identity:

\[ \log 10^{5} = 5 \]

Step 3: State the Result

The exact value of \( \log 10^{5} \) is \( 5 \).

Final Answer

\(\boxed{5}\)

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