Question

pls find the value of xand answer fast ​

Answer 1

Formula used :

$\bullet \sf \: {( \dfrac{a}{b}) }^{m} \: = \: {a}^{m} - \: {b}^{m} \\ \\ \bullet \sf \: {a}^{m} \times {a}^{n} = \: {a}^{m + n} \\ \\ \bullet \sf \: {a}^ { - m} \: = \: \frac{1}{ {a}^{m} } </strong><strong>\</strong><strong>\</strong><strong> </strong>\\ \bullet \sf \: {({a}^{m})}^{n} = {a}^{m \times n}$

Solution :

${ (\dfrac{2 }{3}) }^{3} \times { (\dfrac{2}{3}) }^{5} = \: { (\dfrac{3}{2}) }^{( - 1 - 2x)}$

using identity,

${ (\dfrac{2 }{3}) }^{3 + 5} = \: { (\dfrac{3}{2}) }^{( \: ( - 1)(1 + 2x) \: )} \\ \\ \sf using \: identity \\ { (\dfrac{2 }{3}) }^{8} = \: { (\dfrac{2}{3}) }^{(1 + 2x) }$

comparing power as base are same , we get;

=> 8 = 1+2x

=> 2x = 8 - 1

=> 2x = 7

=> x = 7/2

=> x = (7/2) = 3.5

ANSWER : x = (7/2) = 3.5