Question

(√3)^(x+1)+1=(3√3)^(2x-1)​

Answer 1

GIVEN :–

$\\ \sf \: {( \sqrt{3} )}^{(x + 1)+1} = {(3 \sqrt{3}) }^{2x - 1}$

TO FIND :–

• Value of 'x' = ?

SOLUTION :–

$\\ \sf \implies {( \sqrt{3} )}^{(x + 1)+1} = {(3 \sqrt{3}) }^{2x - 1}$

$\\ \sf \implies {( \sqrt{3} )}^{(x + 2)} = {(3 \sqrt{3}) }^{2x - 1}$

• We should write this as –

$\\ \sf \implies {( \sqrt{3} )}^{(x + 2)} = {( \sqrt{3} .\sqrt{ 3} . \sqrt{3}) }^{2x - 1}$

$\\ \sf \implies {( \sqrt{3} )}^{(x + 2)} = {( \sqrt{3}) }^{3(2x - 1)}$

• Now compare both side –

$\\ \sf \implies x + 2 = 3 (2x - 1)$

$\\ \sf \implies x + 2 = 6x -3$

$\\ \sf \implies x - 6x = - 2 -3$

$\\ \sf \implies - 5x = -5$

$\\ \sf \implies x = \cancel \dfrac{( - 5)}{( - 5)}$

$\\ \implies \large{ \boxed{ \sf x = 1}}$

USED IDENTITY :–

$\\(1) \: \: \sf \: \: {a}^{b} = {a}^{c} \: \: then \: \: { \boxed{ \sf b = c}}$