Question

1). Rozwiąż równanie logarytmiczne:

4 - log x = 3 * √log x

Answer 1

Y = log x

4 - log x = 3 * √log x
4 - y = 3 * √y | ()²
16 + y² - 8y = 9y
y² - 17y + 16 = 0
y₁ = 1
y₂ = 16

log(x₁) = 1
x₁ = 10¹

log(x₂) = 16
x₂ = 10¹⁶

Answer 2

1). Rozwiąż równanie logarytmiczne:

4 - log x = 3 * √log x /()²
(4 - logx)² = (3*√logx)
16 - 8logx + log²x = 9logx
log²x -8logx -9logx + 16 = 0
log²x - 17log x +16 = 0
Wprowadzam dodatkową niewiadomą
logx = t
t² -17t +16 = 0
Δ = (-17)² - 4*1*16 = 289 - 64 = 225
√Δ = √ 225 = 15

t1 = [-( -17 -15)] : 2*1 = (17-15) : 2 = 2 :2 = 1
t2 = [-( -17 +15)] : 2*1 = (17+15) : 2 = 32 :2 = 16

logx = 1 lub logx = 16
z def. log
x = 10¹ lub x = 10¹⁶
x = 10 lub x = 10¹⁶