Question

Solve for x: log6x-log2=1

Answer 1

$log6x-log2=1;\ D:6x > 0\to x > 0\to x\in\mathbb{R^+}\\\\log6x-log2=1\\\\log\left(6x:2\right)=log10^1\\\\3x=10\ /:3\\\\x=\frac{10}{3}\\\\x=3\frac{1}{3}\in D$


$a > 0\ \wedge\ b > 0\ \wedge\ c > 0\ \wedge\ d\in\mathbb{R}\\\\log_ab-log_ac=log_a(b:c)\\\\log_ab=d\iff\ a^d=b\ \ (log_ab=log_aa^d)$

Answer 2

Log(6x/2)=1
Log(3x)=1
This is the same as saying 10^1=3x
10=3x
x=10/3 or 3 and 1/3