સંબંધ અને વિધેય — ગણિત ધોરણ 12 સાયન્સ — Question

${3}^{x}={4}^{x-1}$

$\log_{{2}}{3}^{x}=\log_{{2}}{4}^{x-1}$

$\therefore x\log_{{2}}{3}=(x-1)\log_{{2}}{4}$

$=(x-1)\log_{{2}}{2}^{{2}}$

$={2}(x-1)\log_{{2}}{2}$

$={2}(x-1).1$

$={2}x-{2}$

$\therefore {2}={2}x-x\log_{{2}}{3}$

${2}=x({2}-\log_{{2}}{3})$

$\therefore x=\frac{{2}}{{2}-\log_{2}{3}}$

$=\frac{{2}}{{2}-\frac{1}{\log_{3}{2}}}$

$=\frac{{2}\log_{3}{2}}{{2}\log_{3}{2}-1}$

$=\frac{\log_{3}{2}^{{2}}}{\log_{3}{2}^{{2}}-1}=\frac{\log_{3}{4}}{\log_{3}{4}-1}$

$=\frac{\frac{1}{\log_{4}{3}}}{\frac{1}{\log_{4}{3}}-1}$

$=\frac{1}{1-\log_{4}{3}}$