Question

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

Answer 1

Step-by-step explanation:

this question's answer is x = -1

Answer 2

Required 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:

• $\sf {x}^{a} \times {x}^{b} = {x}^{a + b}$
• $\sf {( {x}^{a}) }^{b} = {x}^{ab}$
• $\sf {x}^{0} = 1 \: \: (x \neq 0)$
• $\sf {x}^{y} = \dfrac{1}{ {x}^{ - y} }$
• $\sf {x}^{a} = {x}^{b} \implies a = b \: \: (x \neq 1)$
• $\sf \dfrac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b}$