Question

if (x/y) n-1=(y/x) n-3 then the value of n is​

Answer 1

Answer:

Step-by-step explanation:

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

(x /y)^( n -1) = (x/y)^{ -(n -3)}

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

we know,

a^m = a ^n

then

m = n

use this here ,

so,

n -1 = 3 -n

2n = 4

n =2 ( answer)

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Answer 2

The value of n = 2

Given :

$\displaystyle \sf{ {\bigg( \frac{x}{y} \bigg)}^{n - 1} = {\bigg( \frac{y}{x} \bigg)}^{n - 3} }$

To find :

The value of n

Solution :

Step 1 of 2 :

Write down the given equation

Here the given equation is

$\displaystyle \sf{ {\bigg( \frac{x}{y} \bigg)}^{n - 1} = {\bigg( \frac{y}{x} \bigg)}^{n - 3} }$

Step 2 of 2 :

Find the value of n

$\displaystyle \sf{ {\bigg( \frac{x}{y} \bigg)}^{n - 1} = {\bigg( \frac{y}{x} \bigg)}^{n - 3} }$

$\displaystyle \sf{ \implies {\bigg( \frac{x}{y} \bigg)}^{n - 1} = {\bigg \{{\bigg( \frac{x}{y} \bigg) }^{ - 1} \bigg \}}^{n - 3} }$

$\displaystyle \sf{ \implies {\bigg( \frac{x}{y} \bigg)}^{n - 1} = {\bigg( \frac{x}{y} \bigg)}^{ - (n - 3)} }$

$\displaystyle \sf{ \implies n - 1 = - (n - 3) }$

$\displaystyle \sf{ \implies n - 1 = - n + 3 }$

$\displaystyle \sf{ \implies 2n = 1 + 3 }$

$\displaystyle \sf{ \implies 2n = 4 }$

$\displaystyle \sf{ \implies n = 2 }$

Hence the required value of n = 2