Fractional Exponents, Logarithms and Number Bases (Extended): แบบฝึกหัด

Solve the equation \(\log_4(2x - 4) = 2\) for \(x\).

Given that \(\log_b 2 = a\) and \(\log_b 3 = c\), express \(\log_b 18\) in terms of \(a\) and \(c\).

Find the sum of all real values of \(x\) that satisfy the following equation:
\(\log_2 x + \log_x 16 = 5\)

Solve for \(x\) in the logarithmic equation: \(\log_3(x + 1) = 2\).

Solve for \(x\) in the exponential equation: \(9^{x+1} = 27^{x-1}\).

Find all real solutions for \(x\) in the equation: \(4^x - 5(2^x) + 4 = 0\).

Solve the following exponential equation for \(x\):
\(3^{x+1} = 81\)

Solve the following exponential equation for \(x\):
\(5^{2x} - 6(5^x) + 5 = 0\)