Ответ:
4) 1,25
5) 4
Пошаговое объяснение:
4)
![1 + log_{0,5}(x - 1) = log_{2}8\\\\1 + log_{0,5}(x - 1) = 3\\\\log_{0,5}(x - 1) = 3 - 1\\\\log_{0,5}(x - 1) = 2\\\\log_{0,5}(x - 1) = log_{0,5}(0,5)^{2}\\\\x - 1 = 0,25\\\\x = 1,25 1 + log_{0,5}(x - 1) = log_{2}8\\\\1 + log_{0,5}(x - 1) = 3\\\\log_{0,5}(x - 1) = 3 - 1\\\\log_{0,5}(x - 1) = 2\\\\log_{0,5}(x - 1) = log_{0,5}(0,5)^{2}\\\\x - 1 = 0,25\\\\x = 1,25](https://tex.z-dn.net/?f=1%20%2B%20log_%7B0%2C5%7D%28x%20-%201%29%20%3D%20log_%7B2%7D8%5C%5C%5C%5C1%20%2B%20log_%7B0%2C5%7D%28x%20-%201%29%20%3D%203%5C%5C%5C%5Clog_%7B0%2C5%7D%28x%20-%201%29%20%3D%203%20-%201%5C%5C%5C%5Clog_%7B0%2C5%7D%28x%20-%201%29%20%3D%202%5C%5C%5C%5Clog_%7B0%2C5%7D%28x%20-%201%29%20%3D%20log_%7B0%2C5%7D%280%2C5%29%5E%7B2%7D%5C%5C%5C%5Cx%20-%201%20%3D%200%2C25%5C%5C%5C%5Cx%20%3D%201%2C25)
5)
0} \atop {x - 3 > 0}} \right. , =>x > 3\\\\log_{4}x(x-3) = log_{4}4\\\\x(x-3) = 4\\\\x^{2} - 3x - 4 = 0\\\\x_{1} = -1\\\\x_{2} = 4" alt="log_{4}x + log_{4}(x - 3) = 1\\\\ODZ: \left \{ {{x > 0} \atop {x - 3 > 0}} \right. , =>x > 3\\\\log_{4}x(x-3) = log_{4}4\\\\x(x-3) = 4\\\\x^{2} - 3x - 4 = 0\\\\x_{1} = -1\\\\x_{2} = 4" align="absmiddle" class="latex-formula">
не входит в ОДЗ, => уравнение имеет один корень x = 4