Question

Solve this (81)^-4 ÷ ( 729) ^(2-x) = 9^4x ​

Answer 1

$\sf\large\underline\blue{Given:-}$

$\\ \sf \to {(81)}^{ - 4} \div {(729)}^{2 - x} = {(9)}^{4x}$

$\sf\large\underline\blue{To\: Find :-}$

• Value of x

$\sf\large\underline\blue{Solution:-}$

Given that,

$↦ {(81)}^{ - 4} \div {(729)}^{2 - x} = {(9)}^{4x}$

$↦\dfrac{ {(81)}^{ - 4}}{{(729)}^{2 - x} } = {(9)}^{4x}$

$↦\dfrac{ {( {3}^{4} )}^{ - 4}}{{({3}^{6})}^{2 - x} } = {( {3}^{2} )}^{4x}$

$↦ \dfrac{ {( {3})}^{ -16 }}{{(3)}^{6(2 - x)} } = {( {3} )}^{8x}$

$↦ \dfrac{ {( {3})}^{ -16 }}{{(3)}^{12- 6x} } = {( {3} )}^{8x}$

$↦{ {( {3})}^{ -16 }}{{(3)}^{ - 12 + 6x} } = {( {3} )}^{8x}$

$↦ { {( {3})}^{ -16 - 12 + 6x }} = {( {3} )}^{8x}$

$↦ { {( {3})}^{ 6x - 28}} = {( {3} )}^{8x}$

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Now, Compare

$↦ 6x - 28 = 8x$

$↦6x - 8x = 28$

$↦ x = - \cancel \dfrac{ 28}{2}$

$↦x = -14$

$\small{\underline{\sf{\blue{Hence-}}}}$

• Value of x is = -14