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Count digits or leading decimal zeros of a power using its characteristic

This type of question, asked 9 times: CDS 2 2016, CDS 1 2017, CDS 2 2018, CDS 1 2019, CDS 2 2019, CDS 1 2020, CDS 2 2023, CDS 2 2025, CDS 2 2026. All 9 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2016

    32
    The number of digits in 3303^{30} is nn and it is given that log⁡103=0.4771\log_{10} 3 = 0.4771. What is the value of nn ?

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  2. Question 2

    CDS 1 2017

    6
    What is the number of digits in 2402^{40} ? (Given that log⁡102=0.301\log_{10} 2 = 0.301)

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  3. Question 3

    CDS 2 2018

    46
    There are n zeros appearing immediately after the decimal point in the value of (0.2)25(0.2)^{25}. It is given that the value of log⁡102=0.30103\log_{10} 2 = 0.30103. The value of n is

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  4. Question 4

    CDS 1 2019

    77
    What is the number of digits in 7257^{25}, 8238^{23} and 9209^{20} respectively ? [Given log⁡102=0.301\log_{10} 2 = 0.301, log⁡103=0.477\log_{10} 3 = 0.477, log⁡107=0.845\log_{10} 7 = 0.845]

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  5. Question 5

    CDS 2 2019

    13
    It is given that log⁡102=0.301\log_{10} 2 = 0.301 and log⁡103=0.477\log_{10} 3 = 0.477. How many digits are there in (108)10(108)^{10} ?

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  6. Question 6

    CDS 1 2020

    3
    How many digits are there in (54)10(54)^{10} ? (Given that log⁡102=0.301\log_{10} 2 = 0.301 and log⁡103=0.477\log_{10} 3 = 0.477)

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  7. Question 7

    CDS 2 2023

    18
    What is number of digits in the expansion of 125100125^{100} ? (Given log⁡102=0.301\log_{10} 2 = 0.301)

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  8. Question 8

    CDS 2 2025

    10
    If log⁡102=0.301\log_{10}2=0.301 and log⁡103=0.477\log_{10}3=0.477, then what is the number of digits in the expansion of 606060^{60}?

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  9. Question 9

    CDS 2 2026

    9
    What is the number of zeros immediately after the decimal point in (0.5)1000(0.5)^{1000} ? (Given that log⁡102=0.30103\log_{10} 2 = 0.30103)

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