Verified answer

1) 4 elevado a x - 12. 2 elevado a x + 32=0

2^x^2 - 12*2^x + 32 = 0

y = 2^x

y^2 - 12y + 32 = 0

(y - 4)*(y - 8) = 0

y1 = 4 --> 2^x1 = 4 --> x1 = 2

y2 = 8 --> 2^x2 = 8 --> x2 = 3

2) 9 elevado a x - 2. 3 elevado a x= 3

3^x^2 - 2*3^x - 3 = 0

y = 3^x

y^2 - 2y - 3 = 0

(y - 3)*(y + 1) = 0

y1 = 3 --> 3^x1 = 3 --> x1 = 1

y2 = - 1 (não serve)

3) 4 elevado x+1- 4 elevado x-1= 60

4*4^x - 4^x/4 = 60

16*4^x - 4^x = 240

15*4^x = 240

4^x = 240/15 = 16 = 4^2

x = 2

4) 5 elevado x -1 + 5 elevado x-2=6

5^x/5 + 5^x/25 = 6

5*5^x + 5^x = 150

6*5^x = 150

5^x = 150/6 = 25 = 5^2

x = 2

5) 3 elevado x+2- 10.3 elevado x + 9=0

9*3^x - 10*3^x + 9 = 0

3^x = 9 = 3^2

x = 2

pronto

1)

2²x-12.2>x+32=0

2>x=y

y²-12y+32=-

y=12+-144-128/2

y=12+-4/2

y'=12+4/2=8

y"=12-4/2=4

x=3

x=2