Math, asked by hassanmeer788, 2 months ago

How many digits does a number 8^n. 53^n+4 have, if n E N?​

Answers

Answered by Dreamsandcats
1

Answer:

To Find :  How many digits number have

Solution:

8ⁿ.5³ⁿ⁺⁴

xᵃ⁺ᵇ = xᵃ.xᵇ

= (2³)ⁿ.5³ⁿ.5⁴

(xᵃ)ᵇ = xᵃᵇ

=2³ⁿ.5³ⁿ.5⁴

xᵃ.yᵃ= (xy)ᵃ

= (2 * 5)³ⁿ.5⁴

= (10)³ⁿ.5⁴

5⁴ = 625

= 625(10)³ⁿ

Hence number of digits = 3n + 3

LETS CHECK

n = 0 Digits   = 3

8ⁿ.5³ⁿ⁺⁴ =  8⁰.5⁴  = 625     3 digits

n = 2   Digits = 8

8².5⁷ =  8⁰.5⁴  = 50,00,000    8 digits

8ⁿ.5³ⁿ⁺⁴  has 3n + 3 digit

Explanation:

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