Question

2log(2a - 1) = 0
How

Answer 1

a = 1

Explanation:

`2\log(2a-1)=0\\\\\text{Domain:}\\\\2a-1>0\qquad\text{add 1 to both sides}\\2a-1+1>0+1\\2a>1\qquad\text{divide both sides by 2}\\(2a)/(2)>(1)/(2)\\\boxed{a>0.5}\\============================\\\\2\log(2a-1)=0\qquad\text{divide both sides by 2}\\\\(2\!\!\!\!\diagup\log(2a-1))/(2\!\!\!\!\diagup)=(0)/(2)\\\\\log(2a-1)=0\qquad\text{use}\ \log_ab=c\iff b=a^c\\\\\log(2a-1)=\log10^0\\\\\log(2a-1)=\log1\iff2a-1=1\qquad\text{add 1 to both sides}\\\\2a-1+1=1+1\\\\2a=2\qquad\text{divide both sides by 2}\\\\(2a)/(2)=(2)/(2)\\\\a=1\in D`