Question

how do you solve 81^x+6 = 243^2x+5

Answer 1

GIVEN :–

$\\ \implies \bf {(81)}^{x+ 6} ={(243)}^{2x+5}$

TO FIND :–

• Value of 'x' = ?

SOLUTION :–

$\\ \implies \bf {(81)}^{x+ 6} ={(243)}^{2x+5}$

• We should write this as –

$\\ \implies \bf {( {3}^{4} )}^{x+ 6} ={({3}^{5})}^{2x+5}$

$\\ \implies \bf {(3)}^{4(x+ 6)} ={(3)}^{5(2x+5)}$

$\\ \implies \bf {(3)}^{4x+24} ={(3)}^{10x+25}$

• Now let's compare –

$\\ \implies \bf 4x+24=10x+25$

$\\ \implies \bf 4x - 10x=25 - 24$

$\\ \implies \bf (4 - 10)x=25 - 24$

$\\ \implies \bf ( - 6)x=25 - 24$

$\\ \implies \bf ( - 6)x=1$

$\\ \implies \bf - 6x=1$

$\\ \implies \large{ \boxed{ \bf x= -\dfrac{1}{6}}}$

Answer 2

${\boxed{\underline{\tt{ \orange{Required \: \: Answer \: \: is \: \: as \: follows:-}}}}}$

◉GIVEN:-

• $\tt{81^{x+6} = 243^{2X+5}}$

◉TO FIND:-

• x

◉ SOLUTION:-

$\leadsto \tt{81^{x+6} = 243^{2X+5}}$

$\leadsto \: \tt{ {( {3}^{4})}^{x + 6} = {( {3}^{5})}^{2x + 5} }$

$\leadsto \tt{ {3}^{4x + 24} = {3}^{10x + 25} }$

Comparing the powers.

$\leadsto \tt{4x + 24 = 10x + 25}$

$\leadsto \tt{24 - 25 = 10x - 4x}$

$\leadsto \tt{6x = - 1}$

$: \implies \: { \boxed{ \underline{ \purple{ \mathbb{x = \frac{ - 1}{6} }}}}}$

HOPE IT HELPS