Find the integer x for which x^5 = 164916224
Answers
Given : X^5=164916224
To find : value of x
Solution:
x⁵ = 164916224
164916224 = 2 * 8,24,58,112
= 2 * 2 * 4,12,29,056
= 2 * 2 * 2 * 2,06,14,528
= 2 * 2 * 2* 2 * 1,03,07,264
= 2 * 2 * 2 * 2 * 2 * 51,53,632
= 2⁵ * 51,53,632
= 2⁵ * 2 * 25,76,816
= 2⁵ * 2 * 2 * 12,88,408
= 2⁵ * 2 * 2 * 2 * 6,44,204
= 2⁵ * 2 * 2 * 2 * 2 * 3,22,102
= 2⁵ * 2 * 2 * 2 * 2 * 2* 1,61,051
= 2⁵ * 2⁵ * 1,61,051
= 4⁵ * 1,61,051
= 4⁵ * 11 * 14,641
= 4⁵ * 11 * 11 * 1,331
= 4⁵ * 11 * 11 * 11 * 121
= 4⁵ * 11 * 11 * 11 * 11 * 11
= 4⁵ * 11⁵
= (44)⁵
164916224 = (44)⁵
=> x⁵ = (44)⁵
=> x = 44
Value of x = 44
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Answer:
In decimal notation, the integers x and x ^5 have the same last digit.
∴ Last digit of x = 4.
1024 × 10^5 < 1649.16224 × 10^5 < 3125 × 10^5
40^5 < 1649.16224 × 10^5 < 50^5
So, 40 < x < 50
⇒ x = 44
Last digit of 4
∴ x = 44
Step-by-step explanation:
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