EXPONENTIALS 1

If 5^(6m-7) x 3^(2n+18) = (9⁴⁴) x (5⁸⁹); Find m and n.

solution

equating equal bases;

5^(6m-7) =  5⁸⁹

5^(6m-7) =  5⁸⁹     [bases are same, they cancel out]

6m - 7 = 89

6m  = 89 + 7

6m  = 96

¹6m  = 96¹⁶

₁6         6₁

m = 16

Again for n we equate equal bases.

3^(2n+18) = 9⁴⁴

3^(2n+18) = (3²)⁴⁴

3^(2n+18) = 3^2x44

3^(2n+18) = 3⁸⁸   [bases are same, they cancel out]

2n + 18 = 88

2n = 88 - 18

2n = 70

2      2

n = 35

Hence m = 16 and n = 35

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

If 6^(2a-19) x 11^(2b+40) = (121⁶⁰) x (6²³); Find a and b.