Question

log3 (4^x + 15*2^x + 27) -2*log3 (4*2^x-3)=0

Answer 1

$log_3(4^x + 15*2^x + 27) -2*log_3 (4*2^x-3)=0\(4^x + 15*2^x + 27)=(4*2^x-3)^2\2^{2x}+15*2^x+27=16*2^{2x}-24*2^x+9\15*2^{2x}-39*2^x-18=0|:3\5*2^{2x}-13*2^x-6=0;2^x=a;a>0\5a^2-13a-6=0\a_{1,2}=frac{13^+_-sqrt{169+120}}{10}=frac{13^+_-17}{10}\a_1=3 ;a_2=-0.4\2^x=3 ; error\x=log_23$

Answer 2

error: a=-0.4,a по условию а>0