EXPONENTIALS 3

If 2^(6m-7) x 3⁽ⁿ⁺⁸⁾ = (3⁴⁶) x (2⁵⁹); Find m and n.

solution

equating equal bases;

2^(6m-7) =  2⁵⁹

2^(6m-7) =  2⁵⁹

6m - 7 = 59

6m  = 59 + 7

6m  = 66

¹6m  =  66¹¹

₁6         6₁

m =  11

again for n we equate equal bases.

3⁽ⁿ⁺⁸⁾ = 3⁴⁶

3⁽ⁿ⁺⁸⁾ = 3⁴⁶

n + 8 = 46

n = 46 - 8

n = 38

Hence m = 11 and n = 38

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

If 5^(2m-17) x 13^(5n+40) = (13⁷⁰) x (5⁴³); Find m and n.