Question

Rozwiązać równanie :

Answer 1

logx 2 + log2 x = 2,5                       x ≠1  i x > 0

log2 2 / log2 x + log2 x = 2,5

1 / log2 x + log2 x = 2,5    / * log2 x

1 + log2 x * log2 x = 2,5 * log2 x

(log2 x)^2 - 2,5 log2 x + 1 = 0

log2 x = t

 

t^2 - 2,5 t + 1 = 0

Δ = 6,25 - 4 = 2,25

√Δ = 1,5

t1 = (2,5 - 1,5)/2 = 1/2

t2 = (2,5 + 1,5)/2 = 4/2 = 2

 

log2 x = 1/2      lub    log2 x = 2

log2 x = log2 2^(1/2)  lub    log2 x = log2 2^2

x = √2       lub                 x = 4