EXPONENTIALS 2

If 2^(6m-7) x 3⁽ⁿ⁺⁵⁾ = (3⁴⁴) x (2²³); Find m and n.

solution

equating equal bases;

2^(6m-7) =  2²³

2^(6m-7) =  2²³

6m - 7 = 23

6m  = 23 + 7

6m  = 30

¹6m  =  30⁵

₁6         6₁

m =  5

again for n we equate equal bases.

3⁽ⁿ⁺⁵⁾ = 3⁴⁴

3⁽ⁿ⁺⁵⁾ = 3⁴⁴

n + 5 = 44

n = 44 - 5

n = 39

Hence m = 5 and n = 39

TRY THIS...............

If 8^(2m-11) x 11⁽ⁿ⁺⁴⁰⁾ = (11⁹⁰) x (8⁴³); Find m and n.