Question

92-1 = 3 x √3(2x+1) has the solution​

Answer 1

$\underline{\large{\sf Answer:}}$

$\sf9^{(x-1)}=3\times\sqrt{3^{(2x+1)}}$

$\sf\:Squaring\:on\:both\:the \:sides$

$\sf(9^{(x-1)})^2=(3\times\sqrt{3^{(2x+1)}})^2$

$\sf\:Apply\:the\:Rule\:(a^m)^n =a^{(m\times n)}\:on\:LHS$

$\implies\sf(9^{(2x-2)})=(3)^2\times3^{(2x+1)}$

$\sf\:Apply\:the\:Rule\:a^m\times b^n=a^{(m+n)}\:on\:RHS$

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

$\implies \sf (3^{(4x-4)})=3^{(2x+3)}$

$\sf\:Now\:Bases\:of\:LHS\:and\:RHS\:are\:equal\:hence\:equate\:the\:powers$

$\implies\sf(4x-4)=(2x+3)$

$\implies\sf 4x-2x=3+4$

$\implies\sf 2x = 7$

$\implies\sf x = (\frac{7}{2})$

Therefore option $\sf( \frac{7}{2})$ is correct