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So. option (b) is incorrect.
If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:
Given, 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
⇒ - log10 (7 x 10)
⇒ - (log10 7 + log10 10)
⇒ - (a + 1)
log10 80 = log10 (8 x 10)
⇒ log10 8 + log10 10
⇒ log10(23) + 1
⇒ 3 log10 2 + 1
⇒ (3 x 0.3010) + 1
⇒ 1.9030
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.
Given expression = 1/log60 3 + 1/log60 4 + 1/log60 5
= log60 (3 x 4 x 5)
= log60 60
= 1.
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