jamesnoah923 jamesnoah923
  • 23-04-2024
  • Mathematics
contestada

8. Given that log 2 = 0.3010 and log 3 = 0.4771. Evaluate log 54.​

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azeemnadeem1283 azeemnadeem1283
  • 23-04-2024

To evaluate \( \log 54 \), we can use the properties of logarithms.

Since \(54 = 2 \times 3^3\), we can rewrite \(54\) as \(2 \times 3^3\).

Using the properties of logarithms, we can express \( \log 54 \) as:

[tex]\[ \log 54 = \log (2 \times 3^3) = \log 2 + \log 3^3 \][/tex]

Given that [tex]\( \log 2 = 0.3010 \) and \( \log 3 = 0.4771 \),[/tex] we substitute these values into the equation:

[tex]\[ \log 54 = 0.3010 + 3 \times 0.4771 \]\[ \log 54 = 0.3010 + 1.4313 \]\[ \log 54 = 1.7323 \]So, \( \log 54 \approx 1.7323 \).[/tex]

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