Question

Решите неравенство ln(2x-1)<=ln(15-3x)

Answer 1

$ln(2x-1)\leq ln(15-3x)\\\\===========================\\\\2x-1 > 0\to2x > 1\to x > \frac{1}{2}\\\\15-3x > 0\to-3x > -15\ \ \ /:(-3)\to x < 5\\\\x\in(\frac{1}{2};\ 5)\\=======================\\\\ln(2x-1)\leq ln(15-3x)\iff2x-1\leq15-3x\\\\2x+3x\leq15+1\\\\5x\leq16\ \ \ /:5\\\\x\leq3\frac{1}{5}\\\\O:x\in(\frac{1}{2};\ 3\frac{1}{5}]$