BdMO National Junior 2007/4
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- Posts:1007
- Joined:Sat Dec 09, 2017 1:32 pm
If $log_{(x+3)}(x^2+15)=2$ then $x=?$
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- Posts:1007
- Joined:Sat Dec 09, 2017 1:32 pm
Re: BdMO National Junior 2007/4
Answer:$\fbox 1$
Solution:
\[log_{(x+3)}(x^2+15)=2\]
\[\Rightarrow (x+3)^2=x^2+15\]
\[\Rightarrow x^2+6x+9=x^2+15\]
\[\Rightarrow 6x=15-9\]
\[\Rightarrow 6x=6\]
\[\Rightarrow x=1\]
Solution:
\[log_{(x+3)}(x^2+15)=2\]
\[\Rightarrow (x+3)^2=x^2+15\]
\[\Rightarrow x^2+6x+9=x^2+15\]
\[\Rightarrow 6x=15-9\]
\[\Rightarrow 6x=6\]
\[\Rightarrow x=1\]