Question

Given:

\[\LARGE \log_5x>\log_{25}(3x-2)\]


Attempted:
\[\LARGE \log_5x>\frac12 \cdot \log_5(3x-2)\]
\[\LARGE 2\cdot \log_5x>\log_5(3x-2)\]
\[\LARGE 2 >{\log_5(3x-2)\over \log_5x}\]
\[\LARGE 2 >\log_x(3x-2)\]
\[\LARGE 2 >\text{Stuck!}\]
Anyway...

Multiple choices are:
\[\LARGE A) \quad x\in (2,\infty )\]
\[\LARGE B) \quad x\in (1,4 )\]
\[\LARGE C) \quad x\in \left(\frac23,1 \right) \cup (2,\infty)\]
\[\LARGE D) \quad x\in \left(\frac23,1 \right) \cup (1,\infty)\]

Answer 1

I have to go now, I'll be back later...