Question

ABC is a triangle. AB = log 8, BC = log 50 and AC = log n where n is a positive integer. Find the number
of possible values of n​

Answer 1

QUESTION IS INCORRECT....................

Answer 2

Answer:

The number of possible values of n​ is 393.

Step-by-step explanation:

Given ABC is a triangle.

Length of AB = log 8

Length of BC = log 50 and

Length of AC = log n

According to the inequality theorem of triangle, the sum of any two sides of a triangle must be greater than the third side.

Applying the condition,

$log8+log50 > logn$

Using the logarithmic rule, $logA+logB = logAB$, we get

$log(8\times 50) > logn$

$\implies log400 > logn$

$\implies 400 > n$

Applying the same rule to the other combination of sides,

$log8+logn > log50$

$\implies log8n > log50$

$\implies 8n > 50$

$\implies n > \dfrac{50}{8} =6.25$

Since n is an integer, therefore $n > 7$

From, 400 > n  and n > 7,

we have the number of possible values of n = 400 - 7 = 393  

Hence, n can take 393 possible values.