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(Q77).If (2.3)^x = (0.23)^y = 1000, then find the value of
1

x
-
1

y

(2.3)^x = (0.23)^y = 1000

2.3 = (1000) ^{1
x}---(A)

0.23 = (1000) ^{1
y} ---(B)

2.3

0.23

=

(1000) ^{1
y}

(1000) ^{1
y}

= (1000) ^{1
x

-

1
y}

10¹ = (³) ^{1
x

-

1
y} ---[(a^m)ⁿ = a^mn]

10¹ = ()³ ^{(

1
x

-

1
y
)}

1 = (

1

x

-

1

y

)

1

= (

1

x

-

1

y

)

(

1

x

-

1

y

) =

1