Quantitative Reasoning : Logarithms

Question

If log₁₀2 = 0.3010, then find how many digits are contained in the number 2⁵⁶?

1. 15
2. 16
3. 17
4. 19
   
   

Correct Answer

Choice (3). 17 digits

Explanatory Answers

Note:

To find the number of digits contained in the number, increment the characteristic (integral part) of the logarithmic value of the number by one.

Taking log of the given number, we get log₁₀2⁵⁶ = 56* log₁₀2 = 56 * 0.3010 = 16.85.

In this case, the characteristic (integral part) = 16.

Therefore, number of digits contained in the number 2⁵⁶ is 16 + 1 = 17.

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