Question

Find the number of digits in 810, given that log 2 = 0.301​

Answer 1

10 Digits would be there in 8¹⁰

Step-by-step explanation:

We need to find the number of digits in 8¹⁰

Let say N = 8¹⁰

Taking Log both sides

Log N = Log (8¹⁰)

=> Log N = 10 Log 8

=> Log N = 10 Log 2³

=> Log N = 10 * 3 Log 2

=> Log N = 30 Log 2

Log 2  = 0.301

=>  Log N = 30 * 0.301

=> Log N = 9.03

Log N  ≥ 9

=> 10 Digits would be there in 8¹⁰

N = 10^(9.03)

for 10ˣ  - numberof digits = x + 1

9 ≤ x < 10  => number of digits = 10

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