Question

The value of x, for which
$\frac{ {125}^{5} }{8} \div \frac{ {125}^{x} }{8} = \frac{ {5}^{18} }{2}$
​

Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

$\sf \dfrac{ {125}^{5} }{8} \div \dfrac{ {125}^{x} }{8} = \dfrac{ {5}^{18} }{2}$

$\sf \longmapsto\large \dfrac{ \frac{ {( {5}^{3} )}^{5} }{8} }{ \dfrac{ { ({5}^{3}) }^{x} }{8} } = \dfrac{ {5}^{18} }{2}$

$\sf \longmapsto \dfrac{ \frac{ {5}^{15} }{ {2}^{3} } }{ \dfrac{ {5}^{3x} }{ {2}^{3} } } = \dfrac{ {5}^{18} }{2}$

$\sf \longmapsto \dfrac{ {5}^{15} }{ {5}^{3x} } = \dfrac{ {5}^{18} }{2}$

Concepts:

• If bases are same then powers gets added in multiplication and gets substracted in division.

$\sf \boxed{ \bold{ \red{ \dfrac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }}}$

$\sf \boxed{\bold {\red{{a}^{m} \times {a}^{n} = {a}^{m + n} }}}$

$\sf \longmapsto \large{5}^{15 - 3x} = \dfrac{ {5}^{18} }{2}$

Bases are same on both sides say 5 so ,5 gets automatically cancelled.

$\sf \longmapsto15 - 3x = \dfrac{18}{2}$

$\sf \longmapsto15 - 3x = 9$

$\sf \longmapsto - 3x = - 6$

$\sf \longmapsto \bold{x = 2}$

Check

$\sf \longmapsto15 - 3x = 9$

$\sf \longmapsto15 - 6 = 9$