Find the value of x for which (4/9)^4*(4/9)^-7=(4/9)^2x-1

1.	Find the value of x for which (4/9)^4*(4/9)^-7=(4/9)^2x-1
Answer» uired Answer:- GIVEN: $\sf { \bigg( \dfrac{4}{9} \bigg)}^{4} \times { \bigg( \dfrac{4}{9} \bigg)}^{ - 7} = { \bigg( \dfrac{4}{9} \bigg)}^{2x - 1}$ To FIND: The value of x. Answer: The value of x is -1. Solution: We have, $\sf \implies { \bigg( \dfrac{4}{9} \bigg)}^{4} \times { \bigg( \dfrac{4}{9} \bigg)}^{ - 7} = { \bigg( \dfrac{4}{9} \bigg)}^{2x - 1}$ $\sf \implies { \bigg( \dfrac{4}{9} \bigg)}^{4 - 7} = { \bigg( \dfrac{4}{9} \bigg)}^{2x - 1} \: \: \blue{ \bigg( {x}^{a} \cdot {x}^{b} = {x}^{a + b} \bigg) }$ $\sf \implies { \bigg( \dfrac{4}{9} \bigg)}^{ - 3} = { \bigg( \dfrac{4}{9} \bigg)}^{2x - 1}$ Comparing BASE, we get, $\sf \implies 2x - 1 = - 3$ $\sf \implies 2x = - 3 + 1$ $\sf \implies 2x = - 2$ $\sf \implies x = - 1$ ★ Hence, the value of x is -1. Formulae To Know: $\sf {x}^{a} \times {x}^{b} = {x}^{a + b}$ $\sf {( {x}^{a}) }^{b} = {x}^{ab}$ $\sf {x}^{0} = 1 \: \: (x \neq 0)$ $\sf {x}^{y} = \dfrac{1}{ {x}^{ - y} }$ $\sf {x}^{a} = {x}^{b} \implies a = b \: \: (x \neq 1)$ $\sf \dfrac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b}$

Answer»

uired Answer:-

GIVEN:

$\sf { \bigg( \dfrac{4}{9} \bigg)}^{4} \times { \bigg( \dfrac{4}{9} \bigg)}^{ - 7} = { \bigg( \dfrac{4}{9} \bigg)}^{2x - 1}$

To FIND:

The value of x.

Answer:

The value of x is -1.

Solution:

We have,

$\sf \implies { \bigg( \dfrac{4}{9} \bigg)}^{4} \times { \bigg( \dfrac{4}{9} \bigg)}^{ - 7} = { \bigg( \dfrac{4}{9} \bigg)}^{2x - 1}$

$\sf \implies { \bigg( \dfrac{4}{9} \bigg)}^{4 - 7} = { \bigg( \dfrac{4}{9} \bigg)}^{2x - 1} \: \: \blue{ \bigg( {x}^{a} \cdot {x}^{b} = {x}^{a + b} \bigg) }$