等式两边同时求对数，可以得到：a * ln3 = b * ln5 = lnk那么，1/a = ln3/lnk，1/b = ln5/lnk所以1/a + 1/b = (ln3 + ln5)/lnk = ln(3*5)/lnk = ln15/lnk = 2lnk = 1/2 * ln15 =ln(15)^(1/2) = ln(√15)所以，k = √15
