Respuesta :

mhanifa

Answer:

  • See below

Step-by-step explanation:

Let the number is x in each case.

Use the property below:

  • logₐc = b ⇒ aᵇ = c or vice versa

We have:

  • [tex]log_3x = 0 -->x = 3^0=1 -->log_31=0[/tex]
  • [tex]log_3x = 1 -->x = 3^1=3 -->log_33=1[/tex]
  • [tex]log_3x = -2 -->x = 3^{-2}=1/9 -->log_3(1/9)=-2[/tex]
  • [tex]log_3x = 4 -->x = 3^4=81 -->log_381=4[/tex]
semsee45

Answer:

[tex]\log_31=0[/tex]

[tex]\log_33=1[/tex]

[tex]\log_3\left(\frac{1}{9}\right)=-2[/tex]

[tex]\log_{3}81=4[/tex]

Step-by-step explanation:

[tex]\textsf{Apply log law}: \quad \log_ax=c \iff x=a^c[/tex]

Therefore:

[tex]\log_3x=0 \implies x=3^0=1[/tex]

[tex]\log_3x=1 \implies x=3^1=3[/tex]

[tex]\log_3x=-2\implies x=3^{-2}=\dfrac{1}{3^2}=\dfrac{1}{9}[/tex]

[tex]\log_3x=4 \implies x=3^4=81[/tex]

Additionally, the logarithm of 1 with any base is always zero:

[tex]\log_a1=0[/tex]

The logarithm of the same number as the base is always 1:

[tex]\log_aa=1[/tex]

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