Question

(4.8)^x=(0.48)^y=1000 then 1/x-1/y=?​

Answer 1

Hello dear my self Ravi Gupta from Ayodhya Uttar Pradesh your question answer and solution is below

Answer:

$\frac{1}{x} - \frac{1}{y} = \frac{1}{3}$

Step-by-step explanation:

$it \: is \: given \: that \\ {(4.8)}^{x} = {(0.48)}^{y} = 1000$

$first \: of \: all \: we \: can \: write \: it \\ {(4.8)}^{x} = 1000 \: \: \: ........(i) \\ \\ and \: {(0.45)}^{y} = 1000 \: \: \: \: \: ........(ii)$

$from \: equation \: (i) \\ 4.8 = {(1000)}^{ \frac{1}{x} } .........(iii)$

$from \: equation \: (ii) \\ {(0.48)}^{y} = 1000 \\ 0.48 = {1000}^{ \frac{1}{y} } ................. (iv)$

$divide \: equation \: (iii) \: by \: (iv) \\ we \: get \: \\ \frac{4.8}{0.48} = \frac{ {1000}^{ \frac{1}{x} } }{ {1000}^{ \frac{1}{y } } } \\ 10 = {1000 }^{ \frac{1}{x} - \frac{1}{y} }$

$10 = ({10}^{3} )^{ \frac{1}{x} - \frac{1}{y } } \\ 10 = {10}^{3( \frac{1}{x} - \frac{1}{y}) }$

$comparing \: power \: on \: both \: side \\ we \: get$

$3( \frac{1}{x} - \frac{1}{y} ) = 1 \\ \frac{1}{x} - \frac{1}{y} = \frac{1}{3}$

Answer 2

Answer:

1/3.

Step-by-step explanation:

(4.8)^x=(0.48)^y=1000

(4.8)^x=1000 , (0.48)^y=1000

4.8=x√1000 , 0.48=y√1000

48/10=1000^1/x (1) , 48/100=1000^1/y (2)

(1)÷(2)

1000^1/x÷1000^1/y=48/10÷48/100

1000^1/x-1/y=10

10^[3(1/x-1/y)] = 10

[3(1/x-1/y)] = 1 (bases are same then powers are equal)

1/x-1/y=1/3.