Question

Find m if $7^{m+1}$ + $7^{m+2}$ = 2744

Answer 1

Given :-

7^(m+1)+7^(m+2) = 2744

To find :-

The value of m

Solution :-

Given that

7^(m+1)+7^(m+2) = 2744

It can be written as

(7^m × 7^1) + (7^m × 7^2) = 2744

Since, a^m × a^n = a^(m+n)

=> (7^m × 7) + (7^m × 49) = 2744

=> 7^m (7+49) = 2744

=> 7^m × 56 = 2744

=> 7^m = 2744/56

=> 7^m = 49

=> 7^m = 7^2

On comparing both sides then

=> m = 2

Therefore, m = 2

Answer :-

The value of m is 2

Check :-

If m = 2 then LHS becomes

7^(2+1) + 7^(2+2)

= 7^3+7^4

= 343+2401

= 2744

= RHS

LHS = RHS is true for m = 2

Used formulae:-

• a^m × a^n = a^(m+n)

Answer 2

$\bold{ANSWER≈}$

Given :

7^(m+1)+7^(m+2) = 2744

To find :

The value of m

Solution :

Given that

7^(m+1)+7^(m+2) = 2744

It can be written as

(7^m x 7^1) + (7^m x 7^2) = 2744

Since, a^m x a^n = a^(m+n) => (7^m x 7) + (7^m x 49) = 2744

=> 7^m (7+49) = 2744

=> 7^m x 56 = 2744

=> 7^m = 2744/56

=> 7^m = 49

=> 7^m = 7^2

On comparing both sides then

=> m = 2

Therefore, m = 2

Answer :

The value of m is 2

Check :

If m = 2 then LHS becomes

7^(2+1) +7^(2+2)

= 7^3+7^4

= 343+2401

= 2744

= RHS

LHS = RHS is true for m = 2

Used formulae: • a^m x a^n = a^(m+n)