Question

Как решить ?
$log_{x}2*log_{0.25x}2=log_{16x}2$

Answer 1

log(x) 2 * log(0.25x) 2 = log(16x) 2

одз

x>0

x<>1

x<>4

x<>1/16

log(a) b = 1/log(b) a

1/log(2) x * 1/log(2) 0.25x = 1/log(2) 16x

log(2) x * log(2) 0.25x = log(2) 16x

log(2) x * ( log(2) x + log(2) 1/4) = log(2) x + log(2) 16

log²(2) x - 2*log(2) x = log(2) x + 4

log²(2) x - 3*log(2) x - 4 = 0

D=9+16=25

log(2) x = (3+-5)/2=-1 4

x=1/2

x=16