Question

. If (a/b)^x-1=(b/a)^x-3 then the value
of x is​

Answer 1

$Given \: \Big(\frac{a}{b}\Big)^{x-1} = \Big(\frac{b}{a}\Big)^{x-3}$

$\implies \Big(\frac{a}{b}\Big)^{x-1} = \Big(\frac{a}{b}\Big)^{-(x-3)}$

/* By Exponential Law */

$\boxed{ \pink{ \Big(\frac{a}{b}\Big)^{n} = \Big(\frac{b}{a}\Big)^{-n} }}$

$\implies x - 1 = - (x-3)$

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

$\implies x - 1 +( x - 3 ) = 0$

$\implies x - 1 + x - 3 = 0$

$\implies 2x - 4= 0$

$\implies 2x = 4$

$\implies x = \frac{4}{2}$

$\implies x = 2$

Therefore.,

$\red{ Value \:of \:x} \green { = 2}$

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