Question

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

Answer 1

The value of x = - 1

Given :

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

To find :

The value of x

Solution :

Step 1 of 2 :

Write down the given equation

The given equation is

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

Step 2 of 2 :

Find the value of x

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

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

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

$\displaystyle \sf{ \implies { \bigg( \frac{4}{9} \bigg)}^{2x - 1} = {\bigg( \frac{4}{9} \bigg)}^{ - 3} }$

Comparing both sides we get

$\displaystyle \sf{ 2x - 1 = - 3 }$

$\displaystyle \sf{ \implies 2x = - 3 + 1 }$

$\displaystyle \sf{ \implies 2x = - 2 }$

$\displaystyle \sf{ \implies x = - 1 }$

Hence the required value of x = - 1

Answer 2

Answer:

THE ANSWER IS IN THE PICTURE