What is the value of $$[\log_{10}(5 \cdot \log_{10} 100)]^2$$?

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Accepted Answer

To solve $$[\log_{10}(5 \cdot \log_{10} 100)]^2$$, start by calculating the components step by step.

**Step 1: Calculate $$\log_{10} 100$$**  
Using the property of logarithms, $$\log_{10} 100 = 2$$, because $$100 = 10^2$$.

**Step 2: Compute $$5 \cdot \log_{10} 100$$**  
Multiply $$5 \cdot \log_{10} 100 = 5 \cdot 2 = 10$$.

**Step 3: Find $$\log_{10}(10)$$**  
Since $$10 = 10^1$$, we know that $$\log_{10}(10) = 1$$.

**Step 4: Square the result**  
Finally, square the value obtained:  
$$(\log_{10}(10))^2 = 1^2 = 1$$.

Thus, the value of the expression is **1**.

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