Logarithmic Equations and Inequalities

1003177802

Level: 
B
Choose the domain of the expression \( \ln\!⁡\left(-|3-2x|+6\right) \).
\( \left(-\frac32,\frac92\right) \)
\( \left(-\infty,-\frac32\right)\cup\left(\frac92,\infty\right) \)
\( \left(-\infty,\frac32\right)\cup\left(\frac92,\infty\right) \)
\( \left(\frac92,\infty\right) \)

1003143202

Level: 
B
What is the total count of all integer solutions of the all following equations? \[ \begin{aligned} \log_{\frac12}\!\left(\log_2⁡x\right)&=-1 \\ \log_5\!\left(\log_{\frac15}⁡x\right)&=0 \\ -\log_{\frac13}\!\left(\log_{\frac12}⁡x\right)&=1 \end{aligned}\]
\( 1 \)
\( 2 \)
\( 3 \)
\( 0 \)