\(2^2 = 2^x\)

\(x = 2\)

\(27^5 = 27^x\)

\(x = 5\)

\(2^{2x} = 2^6\)

\(x = 3\)

\(3^x = 3^2\)

\(x = 2\)

\(4^{2x - 1} = 4\)

\(x = 1\)

\(4^{2x - 3} = 4^{x + 7}\)

\(x = 10\)

\(9^{x - 2} = 9^{3x}\)

\(x = -1\)

\(3^x = 9\)

\(x = 2\)

\(2^x = 4\)

\(x = 2\)

\(8^x = 2\)

\(x = \dfrac{2}{3}\)

\(\left(\dfrac{1}{3}\right)^x = 27\)

\(x = -3\)

\(3^x = 243\)

\(x = 5\)

\(4^x = 2^8\)

\(x = 4\)

\(2^x = 8^3\)

\(x = 9\)

\(4^x = 16\)

\(x = 2\)

\(4^x = \dfrac{1}{16}\)

\(x = -2\)

\(\left(\dfrac{1}{2}\right)^x = 32\)

\(x = -5\)

\(\left(\dfrac{2}{3}\right)^x = \dfrac{4}{9}\)

\(x = 2\)

\(9^x = 27\)

\(x = \dfrac{3}{2}\)

\(2^{2x - 1} = 8\)

\(x = 2\)

\(125^{2x + 1} = 25\)

\(x = \dfrac{-1}{6}\)

\(8^{x + 3} = 16^{x - 1}\)

\(x = 7\)

\(16^{x - 3} = 32\)

\(x = \dfrac{17}{4}\)

\(16^{x - 1} = 64\)

\(x = \dfrac{5}{2}\)

\(10^{x + 1} = 1000\)

\(x = 2\)

\(2^{x + 3} = 256\)

\(x = 5\)

\(4^{3x - 3} = 8^{4x - 4}\)

\(x = 1\)

\(3^{2x + 4} = 27\)

\(x = \dfrac{-1}{2}\)

\(64^{x + 1} = 4\)

\(x = \dfrac{-1}{2}\)

\(3^{x + 2} = 27^{2x}\)

\(x = \dfrac{2}{5}\)

\(4^{x - 2} = 16^{2x + 5}\)

\(x = -4\)

\(4^{x - 5} = 16^{2x - 31}\)

\(x = 19\)

\(5^{x - 4} = 25^{x - 6}\)

\(x = 8\)

\(5^{x + 1} = 125^x\)

\(x = \dfrac{1}{2}\)

\(100^{7x + 1} = 1000^{3x - 2}\)

\(x = \dfrac{-8}{5}\)

\(8^{x - 1} = 32^{3x - 2}\)

\(x = \dfrac{7}{12}\)

\(25^{2x + 3} = 25^{5x - 9}\)

\(x = 4\)

\(27^{x - 2} = 9^x\)

\(x = 6\)

\(9^{2x - 1} = 3^{3x + 3}\)

\(x = 5\)

\(125^{3x - 4} = 25^{4x + 2}\)

\(x = 16\)

\(9^{-x + 5} = 27^{6x - 10}\)

\(x = 2\)

\(5^{5x} = 125^{x + 2}\)

\(x = 3\)

\(9^{2x - 1} = 3^{6x}\)

\(x = -1\)

\(2^{x - 3} = 32\)

\(x = 8\)

\(25^{x + 3} = 5\)

\(x = \dfrac{-5}{2}\)

\(9^{-x + 5} = 27^{6x - 10}\)

\(x = 2\)

\(2 \cdot 3^{2x - 4} = 18\)

\(x = 3\)

\(16^x + 2 = 6\)

\(x = \dfrac{1}{2}\)

\(64^{2x} - 7 = 1\)

\(x = \dfrac{1}{4}\)

\(40 \cdot \left(\dfrac{1}{2}\right)^{x/4} = 5\)

\(x = 12\)

\(40 \cdot \left(\dfrac{1}{4}\right)^{x/3} = 5\)

\(x = \dfrac{9}{2}\)

\(20 \cdot \left(\dfrac{1}{2}\right)^{x/3} = 5\)

\(x = 6\)

\(\left(\dfrac{2}{3}\right)^x = \dfrac{4}{9}\)

\(x = 2\)

\(7^{3t} = \left(\dfrac{1}{49}\right)^{t - 5}\)

\(t = 2\)

\(\left(\dfrac{1}{32}\right)^{x - 1} = 8^x\)

\(x = \dfrac{5}{8}\)

\(\left(\dfrac{1}{27}\right)^{2x - 1} = 9^{x + 1}\)

\(x = \dfrac{1}{8}\)

\(9^x\left(\dfrac{1}{3}\right)^{x + 2} = 27\left(3^x\right)^{-2}\)

\(x = \dfrac{5}{3}\)