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1.

If log 2 = 0.3010, then log 10 is equal to:

Answer» log2 10 = 1 = 1 = 10000 = 1000 . log10 2 0.3010 3010 301
Discussion
2.

If log 2 = 0.3010 and log 3 = 0.4771, the value of log 512 is:

Answer» log5 512 = log 512 log 5 = log 29 log (10/2) = 9 log 2 log 10 - log 2 = (9 x 0.3010) 1 - 0.3010 = 2.709 0.699 = 2709 699 = 3.876
Discussion
3.

If log 2 = 0.30103, the number of digits in 2 is:

Answer» log (264) = 64 x log 2 = (64 x 0.30103) = 19.26592 Its characteristic is 19. Hence, then number of digits in 264 is 20.
Discussion
4.

If = , then:

Answer» ax = by log ax = log by x log a = y log b log a = y . log b x
Discussion
5.

If log = 100 and log = 10, then the value of is:

Answer» log 2 x = 10         x = 210. logx y = 100 y = x100 y = (210)100     [put value of x] y = 21000.
Discussion
6.

The value of log 16 is:

Answer» Let log2 16 = n. Then, 2n = 16 = 24         n = 4. log2 16 = 4.
Discussion
7.

If log 2 = 0.3010, the value of log 80 is:

Answer» log10 80 = log10 (8 x 10) = log10 8 + log10 10 = log10 (23 ) + 1 = 3 log10 2 + 1 = (3 x 0.3010) + 1 = 1.9030.
Discussion
8.

If log 5 + log (5 + 1) = log ( + 5) + 1, then is equal to:

Answer» 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.
Discussion
9.

If log 27 = 1.431, then the value of log 9 is:

Answer» 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.
Discussion