Find the log¹⁰2.7 × 10–2

Answer 1

To find \( \log_{10}(2.7 \times 10^{-2}) \), we can use the properties of logarithms:

1. The logarithm of a product: \( \log_{10}(a \times b) = \log_{10}(a) + \log_{10}(b) \)
2. The logarithm of a power: \( \log_{10}(10^n) = n \)

Using these properties, we can break it down as follows:

\[ \log_{10}(2.7 \times 10^{-2}) = \log_{10}(2.7) + \log_{10}(10^{-2}) \]

Now, calculate each part:

1. \( \log_{10}(10^{-2}) = -2 \)
2. \( \log_{10}(2.7) \) is a value that can be found using a calculator or logarithm table. It's approximately \( 0.431 \).

Putting it all together:

\[ \log_{10}(2.7 \times 10^{-2}) = 0.431 - 2 = -1.569 \]

Thus,

\[ \log_{10}(2.7 \times 10^{-2}) \approx -1.569 \]