Question

Wyznacz x jesli:

a) log1/2 (w indeksie dolnym)(x-4)=-1/2

b)log4(w indeksie dolnym)(3x-10)=1/2

c)logx(w indeksie dolnym)4=2

d)logx-5(w indeksie dolnym) 25=2

e)log4(w indeksie dolnym)(x+3)+log4(w indeksie dolnym)(x+3)=2

f)log1/2(w indeksie dolnym)(x-1)+log1/2(w indeksie dolnym)(x-1)=4

Answer 1

a)

log₁/₂(x-4)=1/2

(1/2)¹/2=x-4

√1/2=x-4

√2/2=x-4

√2/2+4=x

b)log₄(3x-10)=1/2

4¹/²=3x-10

√4=3x-10

2+10=3x

12=3x /:3

x=4

c)

logx4=2

x²=4

x²=2²

x=2

d)

logx₋₅25=2

(x-5)²=25

(x-5)²=5²

x-5=5

x=10

e)

log₄(x+3)+log₄(x+3)=2

log₄(x+3)²=2

4²=(x+3)²

x+3=4

x=4-3

x=1

f)

log ₁/₂(x-1)+log¹/²(x-1)=4

log₁/₂(x-1)²=4

(1/2)⁴=(x-1)²

[(1/2)²]²=(x-1)²

x-1=1/4

x=1 i 1/4