Question

resolva as equaçoes exponenciais

a) 2×+ 2^×-1 = 12

b) 3^×-2 + 3^×+1 = 84

c) 3^2x - 10.3× + 9 = 0​

Answer 1

A)

$2x+2^x-1=12\quad :\quad x=-\frac{2\text{W}_0\left(\frac{e^{\frac{13\ln \left(2\right)}{2}}\ln \left(2\right)}{2}\right)-13\ln \left(2\right)}{2\ln \left(2\right)}\quad \left(\mathrm{Decimal}:\quad x=2.86282\dots \right)$

B)

$3^x-2+3^x+1=84\quad :\quad x=\frac{\ln \left(\frac{85}{2}\right)}{\ln \left(3\right)}\quad \left(\mathrm{Decimal}:\quad x=3.41294\dots \right)$

C)$3^2x-10.3+9=0\quad :\quad x=0.14444\dots$