Question

Find the value of x given that 2 log10(2x-1) =log10 2

Answer 1

$2 log_{10}(2x - 1) = log_{10}(2) \\ log_{10}( {(2x - 1)}^{2} ) = log_{10}(2) \\ {(2x - 1)}^{2} = 2 \\ 2x - 1 = \sqrt{2} \\ 2x = 1 + \sqrt{2} \\ x = \frac{1 + \sqrt{2} }{2}$