Question

plz answer the question correctly​

Answer 1

Answer:

1/3

Step-by-step explanation:

$2.3^{x}=1000\\ 2.3=1000^{1/x}$...........eq1

$0.23^{y} =1000\\0.23=1000^{1/y}$.........eq2

now, divide these two equation.

$2.3/0.23=1000^{1/x}/1000^{1/y} \\10=1000^{(1/x)-(1/y)}\\10=10^{3{(1/x)-(1/y)]}$

1 = 3(1/x)-(1/y)

so, (1/x) -(1/y) =1/3

Answer 2

Answer:

$\dfrac{1}{3}$

Step-by-step explanation:

${\underline{{\text{Given}}}}$

${(2.3)}^{x} = {(0.23)}^{y} = 1000$

${\underline{{\text{To Find:}}}}$

$\dfrac{1}{x} - \dfrac{1}{y}$

${\underline{{\text{Solution:}}}}$

${(2.3)}^{x} = 1000 \\ \\ 2.3 = {1000}^{ \frac{1}{x} } .....(1)$

Again,

${(0.23)}^{y} = 1000 \\ \\ 0.23 = {1000}^{ \frac{1}{y} } .....(2)$

Now,

Dividing (1) by (2)

$\frac{2.3}{0.23} = \frac{( {1000)}^{ \frac{1}{x} } }{ {(1000)}^{ \frac{1}{y} } } \\ \\ \frac{10}{10} \times \frac{2.3}{0.23} = {(1000)}^{( \frac{1}{x} - \frac{1}{y}) } \\ \\ 10 \times \frac{2.3}{2.3} = ( {10}^{3})^{ (\frac{1}{x} - \frac{1}{y}) } \\ \\ 10 = {10}^{3( \frac{1}{x} - \frac{1}{y}) } \\ \\ [\text{Cancelling the 10 from both side}] \\ \\ 1 = 3( \frac{1}{x} - \frac{1}{y} ) \\ \\ \frac{1}{3} = \frac{1}{x} - \frac{1}{y}$

Hence the required answer is 1/3 .

${\underline{{\text{ Some Important Laws of Indices}}}}$

${a}^{n}.{a}^{m}={a}^{(n + m)}$

${a}^{-1}=\dfrac{1}{a}$

$\dfrac{{a}^{n}}{ {a}^{m}}={a}^{(n-m)}$

${({a}^{c})}^{b}={a}^{b\times c}={a}^{bc}$

${a}^{\frac{1}{x}}=\sqrt[x]{a}$

$</p><p>[\text{where all variables are real and greater than 0}]$