In this article we will share TA Exam Maths Topic Logarithm: Formulas and Sample Problems
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TA Exam Maths Topic Logarithm: Formulas and Sample Problems
If a is a positive real number, other than 1 and ab = x, then we write:
b = logax and we say that the value of log x to the base a is b.
Properties of Logarithms:
| Q. If log 27 = 1.431, then the value of log 9 is: | ||||||||
log 27 = 1.431 log (33 ) = 1.431 3 log 3 = 1.431 log 3 = 0.477 log 9 = log(32 ) = 2 log 3 = (2 x 0.477) = 0.954. |
| Q. If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to: | ||||||||
log10 5 + log10 (5x + 1) = log10 (x + 5) + 1 log10 5 + log10 (5x + 1) = log10 (x + 5) + log10 10 log10 [5 (5x + 1)] = log10 [10(x + 5)] 5(5x + 1) = 10(x + 5) 5x + 1 = 2x + 10 3x = 9 x = 3. |
| Q. If log 2 = 0.30103, the number of digits in 264 is: | ||||||||||||||
Its characteristic is 19. Hence, then number of digits in 264 is 20. |
| Q. If log (a/b)+log(b/a) = log (a + b), then: | |||||||||||||||||
log (a/b)+log(b/a) = log (a + b)
So, a + b = 1. |
| Q. The value of log2 16 is: | ||||||||||
Let log2 16 = n. Then, 2n = 16 = 24 n = 4. log2 16 = 4. |
