Question

Solve each equation 1) log5-log2x=1 2) 2log(x+1)=5

Answer 1

$1)\\log5-log2x=1;\ D:x > 0\\\\log(5:2x)=log10\\\\log\frac{5}{2x}=log10\iff\frac{5}{2x}=10\\\\20x=5\ \ \ /:20\\\\x=\frac{1}{4}\in D$


$2)\\2log(x+1)=5;\ D:x+1 > 0\to x > -1\\\\log(x+1)^2=log10^5\iff(x+1)^2=10^5\\\\x+1=-\sqrt{10^5}\ \vee\ x+1=\sqrt{10^5}\\\\x+1=-\sqrt{10^4\cdot10}\ \vee\ x+1=\sqrt{10^4\cdot10}\\\\x=-100\sqrt{10}-1\notin D\ \vee\ x=100\sqrt{10}-1\in D$