Problem: If 9x+2=240+9x9^{x+2}=240+9^{x}9x+2=240+9x, then the value of xxx is:
Answer Choices:
A. 0.10.10.1
B. 0.20.20.2
C. 0.30.30.3
D. 0.40.40.4
E. 0.50.50.5 Solution:
9x+2−9x=240;∴9x(81−1)=240;∴32x=3;∴2x=19^{x+2}-9^{x}=240 ; \quad \therefore 9^{x}(81-1)=240 ; \quad \therefore 3^{2 x}=3 ; \quad \therefore 2 x=19x+2−9x=240;∴9x(81−1)=240;∴32x=3;∴2x=1;
and ∴x=12\therefore x=\dfrac{1}{2}∴x=21.