Question

log 2/3x (дробь две третих) - log3X=3(три в низу)X=3

Answer 1

$log_{2/3}\, x-log_3x=3\; \; ,\; \; \; ODZ:\; x>0\\\\\frac{log_3x}{log_3\frac{2}{3}}-log_3x=3\\\\\frac{log_3x}{log_32-log_33}-log_3x=3\\\\log_3x\cdot (\frac{1}{log_32-1}-1)=3\\\\log_3x\cdot \frac{2-log_32}{log_32-1}=3\\\\log_3x=\frac{3\cdot (log_32-1)}{2-log_32}\\\\x=3^{\frac{3\, (log_32-1)}{2-log_32}}\; \; \; (x\approx 0,4113)$