Question

slove this question step by step​

Answer 1

$\bold{\red{ANSWER}}$

$\boxed{\rm{\pink\:\:x=\frac{1}{2}}}$

$\mathbb{EXPLANATION}$

$\rm{\blue{\rm{Given\:Question\:Is}}}$

$\implies{\rm{9^{x+2}=240+9^x}}$

$\implies{\rm{9^{x+2}-9^x=240}}$

$\implies{\rm{9^x\times9^2-9^2=240}}$

$\boxed{\rm{\pink{Becoz\:\:a^{m+n}=a^m\times\:a^n}}}$

$\implies{\rm{9^x\left(9^2-1\right)=240}}$

$\implies{\rm{9^x\left(81-1\right)=240}}$

$\implies{\rm{9^x\left(80\right)=240}}$

$\implies{\rm{9^x=\frac{240}{80}}}$

$\implies{\rm{9^x=3}}$

$\implies{\rm{3^{2x}=3}}$

$\boxed{\rm{\pink{Now,\:Compare\:Powers\:Of\:3\:We\:Have}}}$

$\implies{\rm{2x=1}}$

$\implies{\rm{x=\frac{1}{2}}}$

$\therefore{x=\frac{1}{2}}$