Решите уравнение (1/5)^x-1+(1/5)^x+1=650

Question

Решите уравнение (1/5)^x-1+(1/5)^x+1=650

Answer 1

(1/5)^x-1+(1/5)^x+1=650

пусть(1/5)^x = t, t >0 тогда

t - 1 + t + 1 = 650
2t = 650
t = 325
(1/5)^x = 325
x = log 1/5 (325)
x = –log 5 (5·5·13)
-x = log 5 (5) + log 5 (5) + log 5 (13)
-x = 2 + log 5 (13)
x = –2 – log 5 (13)