Question

if log(1+x²) base 2x²=1 then find x

Answer 1

Heya

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$log_{2x}(1 + x {}^{2} ) = log_{2x}(2x) \: \: \: \: becoz \: log_{2x}(2x) = 1 \\ \\ \\ 1 + x {}^{2} = 2x \\ \\ \\ {x}^{2} - 2x + 1 = 0 \\ \\ \\ x {}^{2} - x - x + 1 = 0 \\ \\ \\ x(x - 1) - 1(x - 1) = 0 \\ \\ \\ x - 1 = 0 \\ \\ \\ x = 1$