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QUESTION: 1

Which of the following statements is not correct?

Solution:

(a) Since log_{a} a = 1, so log_{10} 10 = 1.

(b) log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3

∴ log (2 + 3) ≠ log (2 x 3)

(c) Since loga 1 = 0. so logio 1 = 0.

(d) log (1 + 2 + 3) = log 6 = log (1 x 2 x 3) = log 1 + log 2 + log 3.

So. (b) is incorrect.

QUESTION: 2

If log 2 = 0.3010 and log 3 = 0.4771, the value of log_{5} 512 is:

Solution:

QUESTION: 3

Solution:

QUESTION: 4

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

Solution:

∴ log 9 = log(3^{2}) = 2 log 3 = (2 x 0.477) = 0.954

QUESTION: 5

Solution:

QUESTION: 6

If log_{10} 7 = a, then is equal to :

Solution:

QUESTION: 7

If log_{10} 2 = 0.3010, then log_{2} 10 is equal to:

Solution:

QUESTION: 8

If log_{10} 2 = 0.3010, the value of log_{10} 80 is:

Solution:

QUESTION: 9

If log_{10} 5 + log_{10} (5*x* + 1) = log_{10} (*x* + 5) + 1, then *x* is equal to:

Solution:

log_{10} 5 + log_{10} (5*x* + 1) = log_{10} (*x* + 5) + 1

⇒ log_{10} 5 + log_{10} (5*x* + 1) = log_{10} (*x* + 5) + log_{10} 10

⇒ log_{10} [5 (5*x* + 1)] = log_{10} [10(*x* + 5)]

⇒ 5(5*x* + 1) = 10(*x* + 5)

⇒ 5*x* + 1 = 2*x* + 10

⇒ 3*x* = 9

⇒ *x* = 3.

QUESTION: 10

The value of is:

Solution:

Given expression= log_{60} 3 + log_{60} 4 + log_{60} 5

= log_{60} (3 x 4 x 5)

= log_{60} 60

= 1.

### Logarithm Formula

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