EXPONENTIALS 9

If 2^(6m-7) x 3⁽ⁿ⁺⁸⁾ = (3⁴⁴) x (2⁶⁵); Find m and n.

solution

equating equal bases;

2^(6m-7) =  2⁶⁵

2^(6m-7) =  2⁶⁵

6m - 7 = 65

6m  = 65 + 7

6m  = 72

¹6m  =  72⁵

₁6         6₁

m =  12

again for n we equate equal bases.

3⁽ⁿ⁺⁸⁾ = 3⁴⁴

3⁽ⁿ⁺⁸⁾ = 3⁴⁴

n + 8 = 44

n = 44 - 8

n = 36

Hence m = 12 and n = 36

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

If 8^(2m-17) x 11^(5n+40) = (11⁷⁰) x (8⁴³); Find m and n.