9th Class Math Chapter 3 Logarithms Short Questions Answer
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9th Class Math Chapter 3 Logarithms Short Questions Answer
log₃ x = 5
3⁵ = x
x = 3⁵
x = 243
log₄ 256 = x
4x = 256
4x = 4⁴
x = 4
log₆₂₅ 5 = ¼ x
(625)1/4x = 5
(5⁴)1/4x = 5
5x = 5¹
x = 1
- log₆₄ x = -2/3
(64)-2/3 = x
(4³)-2/3 = x
4⁻² = x
x = 1/4²
x = 1/16
Solution:
- Log x = 2.4543
x = antilog 2.4543
From the table against the row of 0.45 under 4 we have 2844 and difference under 3 is 2. Adding 2844 and 0 we get 2846.
x = 284.6
- Log x = 0.1821
x = antilog 0.1821
From the table against the row of 0.18 under 2 we have 1521 and difference under 1 is 0. Adding 1521 and 0 we get 1521.
x = 1.521
- Log x = 0.0044
x = antilog 0.0044
From the table against the row of 0.00 under 4 we have 1009 and difference under 4 is 1. Adding 1009 and 1 we get 1010.
x = 1.010
- Log x = 1.6238
x = antilog 1.6238
From the tale against the row of 0.62 under 3 we have 4198 and difference under 8 is 8. Adding 4192 and 8 we get 4206.
x = 0.04206
= log (3 x 3 x 5) = log 3 + log 3 + log 5 = 0.4771 + 0.4771 + 0.6990 = 1.6532 = Log16 – log15 = Log2⁴ – log 3 x 5 = 4 log 2 – log 3 – log 5 = 4(0.3010) – 0.4771 – 0.6999 = 1.6532 = log 48/1000 = log 48 – log1000 = log 3 x 16 – log 10³ = log 3 + log 16 – 3log 10 = 0.4771 + log 2⁴ – 3(1) = 0.4771 + 4 log 2 – 3 = 0.4771 + 4 (0.3010) – 3 = 1.6811 – 3 = 1 + 0.6811 – 3 = – 2 + 0.6811 = 2.6811
Solution: Let x = ³√25.47 x = (25.47)1/3 Taking log on both sides Log x = log (25.47)1/3 Log x = 1/3log 25.47 Log x = 1/3(1.4060) Log x = 0.4686 Taking Antilog on both sides, we get Antilog (Log x) = antilog(0.4686) x = 2.942 Let x = ⁵√342.2 = (342.2)1/5 Taking log on both sides Log x = (342.2)1/5 Log x = 1/5 log 342.2 Log x = 1/5 (2.5343) Log x = 0.5069 Taking Antilog on both sides, we get Antilog (log x) = antilog (0.5069) x = 3.213 Let x = (8.97)³ x (3.95)²/³√15.37 x = (8.97)³ x (3.95)²/(15.37) 1/³ Taking log on both sides, we get Log x = log(8.97)³ x (3.95)²/(15.37)1/³ Log x = log(8.97)³ x (3.95)² – log(15.37)1/³ Log x = log(8.97)³ + log(3.95)² – log(15.37)1/³ Log x = 3 log(8.97) + 2 log (3.95) – 1/3 log(15.37) Log x = 3(0.9528) + 2(0.5966) – 1/3 (1.1867) Log x = 2.8584 + 1.1932 – 0.3956 Log x = 3.6560 Taking antilog on both sides, we get x = antilog (3.6560) x = 4529
