Question

If ${\log }_{1/5}(3x-4)$ is defined, then

• A. $x\in (-4,\infty )$
• B. $x\in (\frac{4}{3},\infty )$
• C. $x\in (\frac{3}{4},\infty )$
• D. $x\in (-\frac{4}{3},\infty )$

Answer 1

The correct option is B $x\in (\frac{4}{3},\infty )$

${\log }_{1/5}(3x-4)$
Base $\frac{1}{5}>0$ and $\frac{1}{5}\ne 1$
$3x-4>0$
$\Rightarrow x>\frac{4}{3}$
$\Rightarrow x\in (\frac{4}{3},\infty )$