EXPONENTIALS 1

If 5^(3m-7) x 3^(2n+18) = (9⁴⁴) x (5⁸⁹); Find m and n.

solution

equating equal bases;

5^(3m-7) =  5⁸⁹

5^(3m-7) =  5⁸⁹     [bases are same, they cancel out]

3m - 7 = 89

3m  = 89 + 7

3m  = 96

¹3m  = 96³²

₁3     3₁

m = 32

Again for n we equate equal bases.

3^(2n+18) = 9⁴¹

3^(2n+18) = (3²)⁴¹

3^(2n+18) = 3^2x41

3^(2n+18) = 3⁸²   [bases are same, they cancel out]

2n + 18 = 82

2n = 82 - 18

2n = 64      [Dividing by 2 both sides]

2      2

n = 32

Hence m = 32 and n = 32

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

If 6^(2a-49) x 11^(2b+60) = (121⁵⁰) x (6²³); Find a and b.