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Use log(8)=0.7740 to approximate the value of log₈(320) log₈(320)

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Final answer:

To approximate log₈(320), we convert to the common logarithm and divide log(320) by log(8), which equals 2.5052/0.7740, resulting in approximately 3.2385.

Step-by-step explanation:

To approximate the value of log₈(320), we first need to recognize that the base 8 logarithm can be converted to the common logarithm (base 10) through change of base formula. Specifically, log₈(320) = log(320) / log(8). Given that log(8) is approximately 0.7740, we can use the common logarithm of 320 to find the value of log₈(320). The common logarithm of 320 lies between the common logarithms of 100 (2) and 1000 (3), suggesting that it will be between 2 and 3. Using a scientific calculator, we find log(320) is approximately 2.5052. Now we can substitute this value into our equation:

log₈(320) = log(320) / log(8) = 2.5052 / 0.7740 ≈ 3.2385

Therefore, log₈(320) is approximately 3.2385 when rounded to four decimal places to match the level of precision given for log(8).

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