Question

Given that 2m + 2n = 9/32

workout mn

Answer 1

Given: $2^m+2^n=\dfrac{9}{32}$

To Find :  mn

Solution:

$2^m+2^n=\dfrac{9}{32}$

$=2^m(1+2^{n-m})=\dfrac{8+1}{2^5}$

$=2^m(1+2^{n-m})=\dfrac{2^3+1}{2^5}$

$=2^m(1+2^{n-m})=2^{-5}(1+2^3)$

on comparing

m = - 5

n - m  = 3

n - (-5) = 3

=> n = - 2  

2⁻⁵ + 2⁻²

= 1/32 + 1/4

= (1 + 8)/32

= 9/32

m = - 5 , n = - 2

mn = (-5)(-2) = 10

Value of mn = 10

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