Question

Ex. bifate va rog mult.

Answer 1

18)
a) (4^x)^2=2^8
4^2x=2^8
2^4x=2^8
4x=8
x=2

b) (10^x)^5 *100=(2^4 * 5^4)^8
10^5x * 10^2=(10^4)^8
10^(5x+2)=10^32
5x+2=32
5x=30
x=6

c) (5^2)^(x+3)=5^4x*5^2
5^(2x+6)=5^(4x+2)
2x+6=4x+2
2x=4
x=2

d) x:(2^3)^0=1
x:2^0=1
x:2=1
x=2

e) (3^x)^5=3^10 * 3^5
3^5x=3^15
5x=15
x=3

f) (7^4)^x=(7^5)^2^2
7^4x=7^20
4x=20
x=5

g) x:(2^2 * 2^3)=4
x:32=4
x=32*4
x=128

h) x+(2^2)^5=2^3 * 2^7
x+2^10=2^10
x=0

20)
a)  3^x+3^(x-1)=4
3^(x-1)(3^1+3^0)=4
3^(x-1)*4=4
3^(x-1)=1
3^(x-1)=3^0
x-1=0
x=1

b)  3^x+3^(x-1)+3^(x-2)+3^(x-3)=40
  3^(x-3) * (3^3+3^2+3^1+3^0)=40
  3^(x-3) * (27+9+3+1)=40
  3^(x-3) * 40=40
  3^(x-3) =1
  3^(x-3) =3^0
x-3=0
x=3