BdMO National Junior 2007/4

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm
BdMO National Junior 2007/4

Unread post by samiul_samin » Sun Feb 24, 2019 8:59 am

If $log_{(x+3)}(x^2+15)=2$ then $x=?$

samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm

Re: BdMO National Junior 2007/4

Unread post by samiul_samin » Sun Feb 24, 2019 1:09 pm

Answer:$\fbox 1$


Solution:
\[log_{(x+3)}(x^2+15)=2\]
\[\Rightarrow (x+3)^2=x^2+15\]
\[\Rightarrow x^2+6x+9=x^2+15\]
\[\Rightarrow 6x=15-9\]
\[\Rightarrow 6x=6\]
\[\Rightarrow x=1\]

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