logarithmic equation

\hspace{-16}$Find Real values of $\bf{x}$ in \\\\$\bf{2012^{\log_{2010}(x-1)}-2010^{\log_{2012}(x+1)}=2}

1 Answers

1057

Ketan Chandak ·2012-05-15 02:46:26

let log₂₀₁₀(x-1)=a (1)
&
log₂₀₁₂(x+1)=b (2)

using (1).....2010^a=x-1
using (2).....2012^b=x+1=x-1+2=2010^a+2

therefore 2012^b-2010^a=2
and acc to question...
2012^a-2010^b=2

thus we get a=b=1... and x=2011

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