Answer

Let , $$y = 125^{100} $$

Log y = 100log125

Log y = 100[log$$\frac{1000}{8}$$]

Log y = 100[log1000 – 3log 2]

Log y =100[ 3 – 3log 2]

Log y =100[ 2.097]

Log y = 209.7 = 210

So, Number of digits is 210.

Answer (D) – 210

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# What is number of digits in the expansion of $$125^{100}$$? (Given $$log_{10}2=0.301$$)

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Question

Answer

Let , $$y = 125^{100} $$

Log y = 100log125

Log y = 100[log$$\frac{1000}{8}$$]

Log y = 100[log1000 – 3log 2]

Log y =100[ 3 – 3log 2]

Log y =100[ 2.097]

Log y = 209.7 = 210

So, Number of digits is 210.

Answer (D) – 210