Question

2^(m+1)+2^(m-1) =80 find the value of m

Answer 1

Answer:

m = 5

Step-by-step explanation:

2ᵐ⁺¹ + 2ᵐ⁻¹ = 80

We know that, aᵐ⁺ⁿ = aᵐ aⁿ , applying it we , get,

=> 2ᵐ 2¹ + 2ᵐ 2⁻¹ = 80

Let 2ᵐ = x , putting in above equation , we get,

=> 2 x + 2⁻¹ x = 80

=> 2 x + ( x / 2 ) = 80

Taking 2 as LCM, we get,

=> ( 4 x + x ) / 2 = 80

=> 5 x / 2 = 80

=> 5 x = 80 × 2

=> x = 160 / 5

=> x = 32

We know that , 32 = 2⁵ , we get,

=> 2ᵐ = 2⁵

Comparing exponent , we get

=> m = 5