Question

The greatest possible value of n could be 9n < 108 if, given that log 3 = 0.4771 and n∈N:
A) 7
B) 8
C) 9
D) 10

Answer 1

7 is the answer
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Answer 2

Correct Question: The greatest possible value of n could be $9^n < 10^8$, if given that log3 = 0.4771 and n ∈ N.

Answer:

Option (B) is the correct answer.

Step-by-step explanation:

Consider the given inequality as follows:

$9^n < 10^8$

Take log on both the sides as follows:

$log(9^n) < log( 10^8)$

$log(3^{2n}) < log( 10^8)$

Using the rules of logarithm, $log(a^b)=b\ log(a)$ and $log10=1$,

⇒ $2n\ log(3) < 8\ log10$

⇒ 2n(0.4771) < 8(1) (Given, log3 = 0.4771)

⇒ 0.9542n < 8 _____ (1)

(A) When n = 7. Then,

From (1), we get

0.9542(7) < 8

6.6794 < 8

The condition is satisfied but 7 is not the greatest value of n.

Thus, option (A) is incorrect.

(B) When n = 8. Then,

From (1), we get

0.9542(8) < 8

7.6336 < 8

So, 8 is the greatest possible value of n.

Thus, option (B) is correct.

(C) When n = 9. Then,

From (1), we get

0.9542(9) < 8

8.5878 < 8, not possible.

Thus, option (C) is incorrect.

(D) When n = 10. Then,

From (1), we get

0.9542(10) < 8

9.542 < 8, not possible.

Thus, option (D) is incorrect.

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