tentang logaritma tolong dijawab secepatnya, thx

jawaban terlampir

mohon koreksi...
senang bisa membantu :)

[tex]2log^2x = 1\\log^2x^2 = 1\\(log x^2)^2 = 1\\log x^2 = 1\\x^2 = 10^1\\x = \sqrt{10}\\\\^xlog(5x^2 - 8x) = 2\\^xlog(5x^2 - 8x) = 2\,\ . \,\ ^xlog x\\^xlog(5x^2 - 8x) =\,\ ^xlog x^2\\5x^2 - 8x = x^2\\4x^2 - 8x = 0\\x^2 - 2x = 0\\x(x - 2) = 0\\x = 0\\x = 2[/tex]

[tex]2\,\ ^2log^2x + 3\,\ ^2logx - 9 = 0\\\text{misal}\,\ ^2logx = a\\2a^2 + 3a - 9 = 0\\(2a - 3)(a + 3) = 0\\a = \frac{3}{2}\\\,\ ^2logx = \frac{3}{2}\\2^{ \frac{3}{2}} = x\\x = \sqrt{8} \\\\a = -3\\\,\ ^2log x = -3\\2^{-3} = x\\x = \frac{1}{8}\\\\^5 log^2x - 9 = 0\\\,\ ^5log^2x - 3^2 = 0\\\,\ (^5 logx + 3)(^5logx - 3) = 0\\^5log x = -3\\5^{-3} = x\\x = \frac{1}{125}\\\\\,\ ^5logx = 3\\x = 5^3\\x = 125 [/tex]