0\ \wedge\ 4x-5 > 0\\x > -1\ \wedge\ x > \frac{5}{4}\\x\in(\frac{5}{4};\ \infty)\\---------------------\\x+1=4x-5\\x-4x=-5-1\\-3x=-6\ \ \ /:(-3)\\x=2\in(\frac{5}{4};\ \infty)\\\\O:x=2" alt="log_5(x+1)=log_5(4x-5)\\-------------------\\x+1 > 0\ \wedge\ 4x-5 > 0\\x > -1\ \wedge\ x > \frac{5}{4}\\x\in(\frac{5}{4};\ \infty)\\---------------------\\x+1=4x-5\\x-4x=-5-1\\-3x=-6\ \ \ /:(-3)\\x=2\in(\frac{5}{4};\ \infty)\\\\O:x=2" align="absmiddle" class="latex-formula">