EXPONENTIAL EQUATIONS 1

If 2^(5m-7) x 3⁽ⁿ⁺⁶⁾ = (3⁴⁴) x (2⁹³); Find m and n.

solution

equating equal bases;

2^(5m-7) =  2⁹³

 

2^(5m-7) =  2⁹³

5m - 7 = 93

5m  = 93 + 7

5m  = 100

¹5m  = 100²⁰

₁5           5₁

m = 20

again for n we equate equal bases.

3⁽ⁿ⁺⁶⁾ = 3⁴⁴

3⁽ⁿ⁺⁶⁾ = 3⁴⁴

n + 6 = 44

n = 44 - 6

n = 38

Hence m = 20 and n = 38

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

If 7^(2m-9) x 11⁽ⁿ⁺⁶⁾ = (11³⁰) x (7²³); Find m and n.