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प्रश्न
If log 2 = 0.3010 and log 3 = 0.4771; find the value of : log 3.6
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उत्तर
We know that log 2 = 0.3010 and log 3 = 0.4771.
log 3.6
= log`36/10`
= log 36 - log 10 ...`[ log_a (m/n) = log_a m - log_a n ]`
= log 2 x 2 x 3 x 3 - 1 ...[ ∵ log 10 = 1 ]
= log 2 x 2 + log 3 x 3 - 1 ...`[ log_a mn = log_a m + log_a n ]`
= log 22 + log 32 - 1 ]
= 2log2 + 2log3 - 1 ...`[ nlog_a m = log_a m^n ]`
= 2(0.3010) + 2(0.4771) - 1
= 1.5562 - 1 ...`[ ∵ log2 = 0.3010 and log 3 = 0.4771 ]`
= 0.5562
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