Find the value of \( \log_{10} r + \log_{10} r^2 + \log_{10} r^4 + \log_{10} r^8 + \log_{10} r^{16} + \log_{10} r^{32} = 63 \)

Given that for sets A and B, in a universal set E, \(A \subseteq B\) then \(A \cap (A \cap B)^{1}\) is

Evaluate \( \frac{1}{3} \div \left[\frac{5}{7}\left(\frac{9}{10}-1+\frac{3}{4}\right)\right] \)

Evaluate \( \frac{0.36 \times 5.4 \times 0.63}{4.2 \times 9.0 \times 2.4} \)

Without using table, solve the equation \(8x^{-2} = \frac{2}{25}\)

Solve for x if 25x + 3(5x) = 4

Evaluate \( \frac{\log_{5}(0.04)}{\log_{3}18-\log_{3}2} \)

Given that \( \sqrt{2} = 1.1414 \), find without using tables, the value of \( \frac{1}{\sqrt{2}} \)

Simplify \( \sqrt{48} - \frac{9}{\sqrt{3}} + \sqrt{75} \)