Question

Resolva ,em R, a seguinte equação exponencial:

$25^x-23*5^x=50$

Answer 1

25^x - 23.5^x = 50

(5^x)² - 23.5^x - 50 = 0 ====> 5^x=y

y² - 23y -50 = 0

∆=(-23)²-4.1(-50)=529+200=729
==>√∆=27
y = -b±√∆/2a
y = 23±27/2
y '= 23+27/2= 50/2 = 25 ✓
y"= 23-27/2= -4/2 = -2 (fora)

5^x = y'
5^x = 25
5^(x) = 5^(2)====> x = 2 ✓