Question

49^n-1
+6 = 7^2n-1 then find the value of n
​

Answer 1

Step-by-step explanation:

49^n-1 +6 = 7^2n-1

7^2(n-1) + 6 = 7^2n-1

7^2n-n + 6 = 7^2n-1

Answer 2

The value of n = 1

Given:

49ⁿ⁻¹ +6 = 7²ⁿ⁻¹

To find:

The value of n

Solution:

Given that 49ⁿ⁻¹ +6 = 7²ⁿ⁻¹  

Here, 49ⁿ⁻¹ = (7²)ⁿ⁻¹ = 7²ⁿ⁻²   [ ∵  7² = 49 ]

Given expression 49ⁿ⁻¹ +6 = 7²ⁿ⁻¹ can be written as

⇒ 7²ⁿ⁻² + 6 = 7²ⁿ⁻¹  

⇒ 7²ⁿ⁻² - 7²ⁿ⁻¹ = - 6 __(1)  

   

Now we can find n value by trial and error method by taking n values

If we take n = 1

7²ⁿ⁻² - 7²ⁿ⁻¹  ⇒ 7²⁽¹⁾⁻² - 7²⁽¹⁾⁻¹

⇒  7⁰ - 7²⁻¹  

⇒ 1 - 7 = - 6       [ ∵ 7⁰ = 1 ]

Here, n = 1 will satisfy (1)

Therefore, we can conclude that value of n = 1

The value of n = 1

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