Computation with the Aid of Logarithms

Computation with the Aid of Logarithms:

We have, log mn = log m + log n
log (m/n) = log m – log n
log mn = 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.

Computation with the Aid of Logarithms Example - Computation with the Aid of Logarithms
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 (23 x 32) + log 26 – 1 – log 54]
⇒ 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

Characteristic and Mantissa of a LogarithmSpontaneous and Non-Spontaneous Process
Principle of Mathematical InductionGibbs Free Energy and Gibbs Helmholtz equation
Demoivre’s TheoremSignificance of Gibbs Free Energy Change
Trigonometric Ratios of Submultiple AnglesAtoms, Molecules and Chemical Arithmetic– NIOS

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