Решение
1.
7^2x-6*7^x+5=0
7^x = t
t²- 6t + 5 = 0
t₁ = 1
t₂ = 5
1) 7^x = 1
7^x = 7^0
x₁ = 0
2) 7^x = 5
xlg7 = lg5
x₂ = lg5 / lg7
2.
4^x+2^x=12
2^2x + 2^x - 12 = 0
2^x = t , t > 0
t² + t - 12 = 0
t₁ = - 4 не удовлетворяет условию t > 0
t₂ = 3
2^x = 3
xlg2 = lg3
x = lg3 / lg2
3.
13^x+1=169^x
13^2x - 13^x - 1 = 0
t = 13^x, t > 0
t² - t - 1 = 0
D = 1 + 4*1*1 = 5
t₁ = (1 - √5)/2 < 0 не удовлетворяет условию t > 0
t₂ = (1 + √5)/2
13^x = (1 + √5)/2
xlg13 = lg[(1 + √5)/2]
x = lg[(1 + √5)/2] / lg13