Question

please solve this of worksheet​

Answer 1

GIVEN :–

$\\ \bf \implies8 \times {3}^{(4x + 3)} + {3}^{11} = {3}^{13}$

TO FIND :–

• Value of 'x' = ?

SOLUTION :–

$\\ \bf \implies8 \times {3}^{(4x + 3)} + {3}^{11} = {3}^{13}$

$\\ \bf \implies8 \times {3}^{(4x + 3)} = {3}^{13} - {3}^{11}$

$\\ \bf \implies8 \times {3}^{(4x + 3)} = {3}^{11}.{3}^{2} - {3}^{11}$

$\\ \bf \implies8 \times {3}^{(4x + 3)} = {3}^{11}({3}^{2} -1)$

$\\ \bf \implies8 \times {3}^{(4x + 3)} = {3}^{11}(9-1)$

$\\ \bf \implies8 \times {3}^{(4x + 3)} = {3}^{11}(8)$

$\\ \bf \implies {3}^{(4x + 3)} = {3}^{11} \times\dfrac{8}{8}$

$\\ \bf \implies {3}^{(4x + 3)} = {3}^{11} \times\dfrac{8}{8}$

$\\ \bf \implies {3}^{(4x + 3)} = {3}^{11}$

• Now let's compare –

$\\ \bf \implies 4x + 3 =11$

$\\ \bf \implies 4x=11 - 3$

$\\ \bf \implies 4x=8$

$\\ \bf \implies x= \cancel \dfrac{8}{4}$

$\\ \large \implies\pink{ \boxed{ \bf x=2}}$

• Hence , The Value of 'x' is 2 .

Answer 2

$\huge \bf \green {\underline{Solution :-}}$

$8 \times {3}^{4x + 3} + {3}^{11} = {3}^{13}$

$⇒8 \times {3}^{4x + 3} = {3}^{13} - {3}^{11}$

$⇒8 \times {3}^{4x + 3} = {3}^{11 + 2} - {3}^{11}$

$⇒8 \times {3}^{4x + 3} = {3}^{11} \times {3}^{2} - {3}^{11}$

$⇒8 \times {3}^{4x + 3} = {3}^{11} ( {3}^{2} - 1)$

$⇒8 \times {3}^{4x + 3} = {3}^{11} \times 8$

$⇒ {3}^{4x + 3} = {3}^{11}$

$⇒4x + 3 = 11$

$⇒4x = 11 - 3$

$⇒4x = 8$

$⇒x = \frac{8}{4}$

$⇒x = 2$

$\sf \red{Hence, \: the \: value \: of \: x \: is \: 2. }$