Question

resolva as equações exponenciais acima! ajudaa

Answer 1

15)⁴√ 3^x=³√3²
3^x/4=3^2/3
x/4=2/3
3x=4.2
x=8/3

16)2³(2x+1)= ³√2²(2x-1)

2^6x+3=³√ 2^2x-2

2^6x+3= 2^2x-2/3

3(6x+3)= 2x-2

18x+9=2x-2

18x-2x= -2-9

16x= -11
x=-11/16

17)2^x²-x-16=2⁴
x²-x-16=4
x²-x-16-4=0
x²-x-20=0
∆=(-1)²-4.1.(-20)
∆=1+80
∆=81
x=-(-1)±√81/2.1
x= 1±9/2
x1=10/2=5
x2=1-9/2=-8/2=-4

18)3^x²+2x=3^5
x²+2x=5
x²+2x-5=0
∆=2²-4.1.(-5)
∆=4+20
∆=24
x=-2±√24/2.1
x=-2±√24/2
x= -2±2√6/2
x1=-2+2√6/2= -1+1√6
x2=-2-2√6/2=-1-1√6

19)5^2x²+3x-2=5°
2x²+3x-2=0
∆=3²-4.2.(-2)
∆=9+16
∆=25
x=-3±√25/2.2
x=-3±5/4
x1=-3+5/4=-2/4=-1/2
x2=-3-5/4=-8/4= -2