Question

solve this equation.​

Answer 1

Answer:

Formula lagao

Step-by-step explanation:

toh apne ap aa jayega

Answer 2

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

$\sf \longmapsto { \bigg( \dfrac{3}{2} \bigg )}^{6} \div { \bigg( \dfrac{3}{2} \bigg )}^{2n + 1 } \times { \bigg( \dfrac{3}{2} \bigg )}^{ - 3} = 1$

Concepts

When bases are and powers are different then their powers gets added during multiplication and gets substracted during division.

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

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

$\sf \longmapsto{ \bigg( \dfrac{3}{2} \bigg )}^{6 - (2n + 1)} \times { \bigg( \dfrac{3}{2} \bigg )}^{ - 3} = 1$

$\sf \longmapsto{ \bigg( \dfrac{3}{2} \bigg )}^{6 - 2n - 1} \times { \bigg( \dfrac{3}{2} \bigg )}^{ - 3} = 1$

$\sf \longmapsto{ \bigg( \dfrac{3}{2} \bigg )}^{5 - 2n} \times { \bigg( \dfrac{3}{2} \bigg )}^{ - 3} = 1$

Now,here bases are same so ,their powers gets added:

$\sf \longmapsto{ \bigg( \dfrac{3}{2} \bigg )}^{5 - 2n + ( - 3)} = 1$

$\sf \longmapsto{ \bigg( \dfrac{3}{2} \bigg )}^{2 - 2n} = 1$

$\sf \boxed{\bold{ {a}^{0} = 1}}$

$\sf \longmapsto{ \bigg( \dfrac{3}{2} \bigg )}^{2 - 2n} = { \bigg( \dfrac{3}{2} \bigg )}^{0}$

Now ,comparing with the coefficient to both sides :

$\sf \longmapsto2 - 2n = 0$

$\sf \longmapsto - 2n = - 2$

$\sf \longmapsto2n = 2$

$\sf \boxed{\bold{n = {\red{1}}}}$