Question

x log10 3= (x-2)log10 5

Answer 1

$x log_{10}(3) = (x - 2) log_{10}(5) \\ log_{10}( {3}^{x} ) = log_{10}( {5}^{x - 2} ) \\ {3}^{x} = {5}^{x - 2} = {5}^{x} \times {5}^{ - 2} \\ \frac{ {5}^{x} }{ {3}^{x} } = {5}^{2} \\ {( \frac{5}{3}) }^{x} = 25 \\ x = \frac{ log(25) }{ log( \frac{5}{3} ) }$