Question

a^x=(a/k)^y=k^m, then 1/x - 1/y =​

Answer 1

Answer:

1/m

Step-by-step explanation:

a^x = k^m  =>  a^(xy) = k^(my)

(a/k)^y = k^m  =>  a^y = k^(m+y)  =>  a^(xy) = k^(mx+xy)

Therefore

k^(my) = k^(mx+xy)

=> my = mx + xy

=> m(y - x) = xy

=> m(1/x - 1/y) = 1

=> 1/x - 1/y = 1/m

Answer 2

$good \: morning \: \\ \\ \\ \\ let \: \: \: \: \\ \\ a {}^{x} = (a \div k) {}^{y} = k {}^{m} = z \\ \\ \\ \\ = > \\ \\ \\ a {}^{x} = z \: \: \: \: \: \: \: \: (a \div k) {}^{y} = z \\ \\ \\ and \: \: \: \: \: k {}^{m} = z \\ \\ \\ \\ = > \\ \\ \\ a = z {}^{(1 \div x)} \: \: \: \: \: (a \div k) {}^{} = z {}^{1 \div y} \\ \\ and \: \: \: \: \: \: k = z {}^{1 \div m} \\ \\ \\ \\ = > \\ \\ \\ z {}^{(1 \div y)} = z {}^{(1 \div x)} \times z {}^{( - 1 \div m)} \\ \\ \\ \\ = > \\ \\ (1 \div y) = (1 \div x) - (1 \div m) \\ \\ \\ = > \\ \\ \\ \\ (1 \div x) - (1 \div y) =( 1 \div m)$