Question

If 6^(n+4) =36^(4n+7) then the value of n is: *

Answer 1

Answer:

n = -10/7

Step-by-step explanation:

6^(n+4) = 36^(4n+7)

=> 6^(n+4) = [6²]^(4n+7)

=> 6^(n+4) = 6^(8n+14)

=> n+4 = 8n+14

=> 4-14 = 8n-n

=> 7n = -10

=> n = -10/7

Answer 2

The value of n will be -10/7.

Given:

an equation: 6⁽ⁿ⁺⁴⁾ = 36⁽⁴ⁿ⁺⁷⁾

To Find:

we need to find the value of n in the given equation

Solution:

we know that the square of 6 is 36

⇒ 36⁽⁴ⁿ⁺⁷⁾ = 6²⁽⁴ⁿ⁺⁷⁾

= 6⁽⁸ⁿ⁺¹⁴⁾

thus, the equation will become-

6⁽ⁿ⁺⁴⁾ = 6⁽⁸ⁿ⁺¹⁴⁾

now as the bases on both sides are equal, the powers will be the same

⇒ n + 4 = 8n + 14

taking the like terms to one side, we get-

n - 8n = 14 - 4

-7n = 10

-n = 10/7

n = -10/7

Thus, the value of n will be -10/7.

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