Question

2to the power of n+1 +2to the power of n=24,find the value of n​

Answer 1

Step-by-step explanation:

Given:-

2^(n+1) + 2^n = 24

To find:-

Find the value of n ?

Solution:-

Given that

2^(n+1) + 2^n = 24

We know that

a^m×a^n = a^(m+n)

=> 2^n × 2^1 + 2^n = 24

=> 2^n × 2 + 2^n = 24

=> 2^n ( 2+1) = 24

=> 2^n × 3 = 24

=> 2^n = 24/3

=> 2^n = 8

=> 2^n = 2×2×2

=> 2^n = 2^3

On Comparing both sides then

n = 3

Answer:-

The value of n for the given problem is 3

Check:-

If n = 3 then

LHS = 2^(3+1)+2^3

=> 2^4 + 2^3

=> (2×2×2×2)+(2×2×2)

=> 16+8

=> 24

=> RHS

LHS = RHS is true for n=3

Used formula:-

• a^m×a^n = a^(m+n)

Answer 2

Answer:

n+1²=24

or,n+1= √24

or,n+1= √2×2×2×3

or,n+1=2√6

or,n=2√6-1

or,n=1√6