EXPONENTIALS 1

If 5^(6m-7) x 3^(2n+22) = (3⁴⁴) x (5⁵³); Find m and n.

Solution

Equating equal bases;

5^(6m-7) =  5⁵³

5^(6m-7) =  5⁵³

6m - 7 = 53

6m  = 53 + 7

6m  = 60

¹6m  = 60¹⁰

₁6         6₁

m = 10

again for n we equate equal bases.

3^(2n+22) = 3⁴⁴

3^(2n+22) = 3⁴⁴

2n + 22 = 44

2n = 44 - 22

2n = 22

2       2

n = 11

Hence m = 10 and n = 11

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

If 8^(2x-19) x 13^(2y+40) = (13⁶⁶) x (8⁴³); Find x and y.