Tentukan himpunan penyelesaian dari log 2 (x)-log (x¹¹⁰)+1000=0

Tentukan himpunan penyelesaian dari log 2 (x)-log (x¹¹⁰)+1000=0

$log^2(x)-log(x^{110})+1000 = 0\ big(log(x)big)^2-110log(x)+1000 = 0$

misal: $t = log(x)$

$t^2-110t+1000 = 0\ (t-100)(t-10) = 0\ t-100 = 0 vee t-10 = 0\ t = 100 vee t = 10\ log(x) = 100 vee log(x) = 10\ log(x) = 100 cdot log(10) vee log(x) = 10 cdot log(10)\ log(x) = log(10^{100}) vee log(x) = log(10^{10})\ x = 10^{100} vee x = 10^{10}$

Jawaban:

x = { 10¹⁰⁰ atau 10¹⁰ }