EXPONENTIAL EQUATIONS - 2

If 2^(6m-7) x 3⁽ⁿ⁺⁹⁾ = (3⁴⁴) x (2⁹³); Find m and n.

solution

equating equal bases;

2^(6m-7) =  2⁹³

2^(6m-7) =  2⁹³

6m - 7 = 93

6m  = 93 + 7

6m  = 100

¹6m  = 100⁵⁰

₁6           6₃

m = ⁵⁰/₃

again for n we equate equal bases.

3⁽ⁿ⁺⁹⁾ = 3⁴⁴

3⁽ⁿ⁺⁹⁾ = 3⁴⁴

n + 9 = 44

n = 44 - 9

n = 35

Hence m = 20 and n = 35

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

If 8^(2m-9) x 11⁽ⁿ⁺⁴⁰⁾ = (11⁶⁰) x (8²³); Find m and n.