Question

usando a definição de logaritimos, determine x em cada caso:

A - logₓ 1000 = 3

B - log₀,₀₄ 125 = X

C - log₈ √32 = y

H - log₁₀₀₀ 0,001 = z ​

Answer 1

Resposta:

logₓ  a=b  ==> a=xᵇ

A)

1000=x³

10³=x³

x=10

B)

125=0,04ˣ

125=(4/100)ˣ

5³=(1/5²)ˣ

5³=(5⁻²)ˣ

5³=5⁻²ˣ

3=-2x

x=-3/2

C)

log₈  √2⁵

log ₈ 2^(5/2) =y

log 2^(5/2) /log 8 =y

log 2^(5/2) /log 2³ =y

(5/2) *log 2 / 3*log 2 =y

(5/2)  / 3=y

y=5/6

H)

log₁₀₀₀ 0,001 = z ​

log 0,001 /log 1000= z ​

log 10⁻³ /log 10³ =z

(-3) * log 10 /3*log 10=z

(-3)/3=z

z=-1