Question

If 2^n+m=16and4^n-m1/32 find the value of n+m

Answer 1

Step-by-step explanation:

Given:-

2^(n+m)=16 and 4^(n-m)=1/32

To find :-

Find the value of n+m?

Solution:-

Given that:

2^(n+m)=16

=>2^(n+m)=2^4

Since bases are equal then exponents must be equal.

=>n+m=4------(1)

and

4^(n-m)=1/32

=>(2^2)^(n-m)=1/2^5

(since (a^m)^n=a^mn)

=>2^2(n-m)=1/2^5

(since 1/a^n=a^-n)

=>2^2(n-m)=2^-5

Since bases are equal then exponents must be equal.

2(n-m)=-5

=>n-m=-5/2-----(2)

from (1)&(2)

n+m=4

n-m=-5/2

(+)

_________

2n+0=4-5/2

________

=>2n=(8-5)/2

=>2n=3/2

=>n=3/4

from (1)

(3/4)+m=4

=>m=4-(3/4)

=>m=(16-3)/4

=>m=13/4

The values of m and n are 13/4 and 3/4 respectively

Answer:-

The values of m,n and n+m are

m= 13/4

n= 3/4

n+m=4 respectively.