Evaluate log(1011⋅105)

Answer 1

To evaluate \( \log(1011 \cdot 105) \), we can use the property of logarithms that states:

\[ \log(a \cdot b) = \log a + \log b \]

Applying this property, we get:

\[ \log(1011 \cdot 105) = \log(1011) + \log(105) \]

Next, we can compute \( \log(1011) \) and \( \log(105) \) using a calculator (or logarithm tables) or approximate these values using known logarithms.

Using approximate values:

\[ \log(1011) \approx 3.0043 \quad \text{(since 1011 is slightly more than 1000)} \]

\[ \log(105) \approx 2.0212 \quad \text{(since \( 10^2 = 100 \) and \( 10^3 = 1000 \), and \( 105 \) is slightly above \( 100 \))} \]

Now we can add these two results together:

\[ \log(1011 \cdot 105) \approx 3.0043 + 2.0212 = 5.0255 \]

Therefore, the final evaluation gives us:

\[ \log(1011 \cdot 105) \approx 5.0255 \]

So, the answer is approximately:

\[ \boxed{5.0255} \]