EXPONENTIALS 1

If 5^(6m-7) x 3^(2n+18) = (3⁴⁴) x (5⁹³); Find m and n.

solution

equating equal bases;

5^(6m-7) =  5⁹³

5^(6m-7) =  5⁹³

6m - 7 = 93

6m  = 93 + 7

6m  = 100

¹6m  = 100⁵⁰

₁6           6₃

m = ⁵⁰/₃

again for n we equate equal bases.

3^(2n+18) = 3⁴⁴

3^(2n+18) = 3⁴⁴

2n + 18 = 44

2n = 44 - 18

2n = 26

2      2

n = 13

Hence m = 50/3 and n = 13

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

If 8^(2x-19) x 11^(2y+40) = (11⁶⁰) x (8²³); Find x and y.