Question

Помогите пожалуйста)
а) 3ˣ⁺¹ - 3ˣ = 18
б) log₂x + log₄x = 6
в) log1/3(log₃x) = -1

Answer 1

$3^{x+1}-3^x=18$
$3^x*3-3^x=18$
$2*3^x=18$
$3^x=9$
$3^x=3^2$
$x=2$


$log_2 x+log_4 x=6$
ОДЗ: x>0
$log_2 x+log_{2^2} x=6$
$log_2 x+ frac{1}{2} log_2 x=log_2 2^6$
$frac{3}{2} log_2 x=log_2 2^6$
$x^{frac{3}{2}}=2^6/tex] [tex]x=(2^6)^{frac{2}{3}}$
$x=2^4=16$


$log_{ frac{1}{3} }(log_3 x)=-1$
ОДЗ: $left { {{log_3 x textgreater 0 } atop {x textgreater 0}} right. ;left { {{log_3 x textgreater log_3 1 } atop {x textgreater 0}} right. ;left { {{ x textgreater 1 } atop {x textgreater 0}} right. ;x textgreater 1$
$log_{ frac{1}{3} }(log_3 x)=log_{ frac{1}{3} }3$
$log_3 x=3$
$log_3 x=log_3 27$
$x=27$