## Computation with the Aid of Logarithms:

We have, log mn = log m + log n log (m/n) = log m – log n log m ^{n} = n log m |

Thus, in logarithms, multiplication is tackled by addition, division by subtraction and the operation of replaced multiplication of the same number by a single multiplication. As the latter processes are easier than the former ones, logarithms provide us with an opportunity to perform operations of multiplication and division with much ease.

Example- Find the value of [(7.2 x 6.4)/62.5]^{1/3} correct to three places of decimal, given that log 2 = 0.30103, log 3 = 0.47712 and log 90.34 = 1.95588.Solution- Let x = [(7.2 x 6.4)/62.5]^{1/3}x = (72/10 x 64/10 x 10/625) ^{1/3}Apply Log- log x = 1/3 log [(72 x 64)/(625 x 10)] ⇒ log x = 1/3 [log 72 + log 64 – log 10 – log 625] ⇒ log x = 1/3 [log (2 ^{3} x 3^{2}) + log 2^{6} – 1 – log 5^{4}]⇒ log x = 1/3 [3 log 2 + 2 log 3 + 6 log 2 – 1 – 4 log (10/2)] ⇒ log x = 1/3 [9 log 2 + 2 log 3 – 1 – 4 {log 10 – log 2}] ⇒ log x = 1/3 [9 log 2 + 2 log 3 – 1 – 4 + 4 log 2] ⇒ log x = 1/3 [13 log 2 + 2 log 3 -5] ⇒ log x = 1/3 [13 (0.30103) + 2 (0.47712) – 5] ⇒ log x = 1/3 [3.91339 + 0.95424 – 5] ⇒ log x = 1/3 [4.86763 – 5] ⇒ log x = 1/3 [- 0.13237] ⇒ log x = – 0.04412 ⇒ log x = (- 0.04412 + 1) – 1 ⇒ log x = -1 + 0.95588 Apply Antilog- x = 0.9033 |

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