Question

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

Answer 1

$HEYA \: \\ \\ GIVEN \: \: QUESTION \: \: Is \: \: \\ \\ ( \frac{a}{b} ) {}^{(x - 1)} = ( \frac{b}{a} ) {}^{(x - 3)} \\ \\ ( \frac{a}{b} ) {}^{(x - 1)} = ( \frac{a}{b} ) {}^{ - (x - 3)} \\ \\ ( \frac{a}{b} ) {}^{(x - 1)} = ( \frac{a}{b} ) {}^{(3 - x)} \\ \: compare \: \: powers \: of \: \frac{a}{b} \: we \: have \\ \\ x - 1 = 3 - x \\ \\ x + x = 3 + 1 \\ \\ 2x = 4 \\ \\ x = \frac{4}{2} \\ \\ x = 2 \\ \\ Note \: \: \\ \\ ( \frac{x}{y} ) = ( \frac{y}{x} ) {}^{ - 1}$