PYQ Vault
EbooksTutor

Number of digits in a^n, given log 2 and log 3

The same question, asked 7 times: CDS 2 2016*, CDS 1 2017*, CDS 1 2019*, CDS 2 2019*, CDS 1 2020*, CDS 2 2023*, CDS 2 2025. Every wording 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 ?

    Tap an option to check your answer.

  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)

    Tap an option to check your answer.

  3. Question 3

    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]

    Tap an option to check your answer.

  4. Question 4

    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} ?

    Tap an option to check your answer.

  5. Question 5

    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)

    Tap an option to check your answer.

  6. Question 6

    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)

    Tap an option to check your answer.

  7. Question 7

    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}?

    Tap an option to check your answer.