Log 的難題

圖片參考：https://s.yimg.com/lo/api/res/1.2/ZQit8r6YM3UMER1bF6V.OQ--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/http://i.imgur.com/ZH9B85L.gif

log_3(x) + log_x(9) = 3

log(x)/log(3) + log(9)/log(x) = 3

log(x)/log(3) + log(3²)/log(x) = 3

log(x)/log(3) + 2log(3)/log(x) = 3

log(3) log(x) [ log(x)/log(3) + 2log(3)/log(x) ] = 3 log(3) log(x)

[log(x)]² + 2[log(3)]² = 3 log(3) log(x)

[log(x)]² - 3 log(3) log(x) + 2[log(3)]² = 0　　a² - 3ab + 2b²

[log(x) - 2 log(3)][log(x) - log(3)] = 0　　　(a - 2b)(a - b)

log(x) = 2 log(3) or log(x) = log(3)

log(x) = log(3²) or log(x) = log(3)

log(x) = log(9) or log(x) = log(3)

x = 9 or x = 3



圖片參考：https://s.yimg.com/rk/HA00430218/o/868456363.jpg