Question

If (2.3)=(0.23)^y = 1000 then find the value of 1 by x -1 by y

Answer 1

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

$\implies (2.3)^{x} = (0.23)^{y} = 10^{3}$

$i) (2.3)^{x} = 10^{3}$

$\implies 2.3 = (10)^{\frac{3}{x}}\: ---(1)$

$ii) (0.23)^{y} = 10^{3}$

$\implies 0.23 = (10)^{\frac{3}{y}}\: ---(2)$

/* Do (1) ÷ (2) , we get */

$\frac{10^{\frac{3}{x}}}{10^{\frac{3}{y}}} = \frac{2.3}{0.23}$

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

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

$\boxed { \pink { If \: a^{m} = a^{n} \implies m = n }}$

$\implies 3[\frac{1}{x} - \frac{1}{y}] = 1$

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

Therefore.,

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

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Answer 2

Answer:

hope this helps you :)

Step-by-step explanation: