Equations And Inequalities Question 39
Question: The equation $ {\log_3}(3^{x}-8)=2-x $ has the solution
Options:
A) $ x=1 $
B) $ x=2 $
C) $ x=3 $
D) $ x=4 $
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ {\log_3}(3^{x}-8)=2-x\Rightarrow 3^{x}-8={3^{2-x}} $ where $ 3^{x}-8>0 $
$ \Rightarrow 3^{x}-8=\frac{9}{3^{x}}\Rightarrow {{(3^{x})}^{2}}-8(3^{x})-9=0 $
$ \Rightarrow (3^{x}+1)(3^{x}-9)=0\Rightarrow 3^{x}=9[\because ,3^{x}\ne -1] $
$ \therefore x=2 $
BETA
