Question

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If (a/b)^x-1 = (b/a)^x-3, then x =?
a) 0. b) 1. c) 2. d) 3

Answer 1

Hey Friend ☺

( a/b )^x - 1 = ( b/a )^x - 3

》( a/b )^x - 1 = ( a/b )^ 3 - x

Since a^m = 1/a^- m

So bases are same we can write indices equal

》x - 1 = - x + 3

》x + x = 3 + 1

》2x = 4

》x = 4/2

》x = 2

So the value of x is 2

choose option c)

Hope it helps you ..!!

✌

Answer 2

${ (\frac{a}{b} )}^{(x - 1)} = { (\frac{b}{a}) }^{(x - 3)} \\ \\ = > { (\frac{a}{b}) }^{x} \times { \frac{b}{a} }^{1} = {( \frac{b}{a}) }^{x} \times { (\frac{a}{b}) }^{3} \\ \\ = > { (\frac{a}{b}) }^{x} \times { (\frac{a}{b} )}^{x} = { (\frac{a}{b}) }^{3} \times \frac{a}{b} \\ \\ = > { (\frac{a}{b} )}^{2x} = { \frac{a}{b} }^{3 + 1} \\ \\ = > 2x = 4 \\ \\ = > x = 2$

hence, option (c) is correct

I HOPE ITS HELP YOU DEAR,
THANKS