Question

ftom rs aggarwl of standerd 9​

Answer 1

Question:-

$\sf( \sqrt{ \frac{3}{5} } ) {}^{x - 1} = ( \frac{27}{125} ) {}^{ - 1}$

Solution:-

$\sf( \sqrt{ \frac{3}{5} } ) {}^{x - 1} = ( \frac{27}{125} ) {}^{ - 1}$

$\longmapsto \sf \: ( \frac{3}{5} ) {}^{ \frac{x - 1}{2} } = ( \frac{3 {}^{3} }{5 {}^{3} } ) {}^{ - 1}$

$\longmapsto \sf \: ( \frac{3}{5} ) {}^{ \frac{x - 1}{2} } = ( \frac{3}{5} ) {}^{ - 3}$

$\therefore \sf \: \frac{x - 1}{2} = - 3$

$\longmapsto \sf \: x - 1 = - 6$

$\longmapsto \sf \: x = - 6 + 1 = - 5$

$\longmapsto \sf \: x = - 5$

Answer:-

• $\red\longmapsto \sf \huge\underline \mathfrak \red{x = - 5}$