Question

HELP PLEASE
Write each number as a logarthm with base 3.
0
1
-2
4

Answer 1

`\log_31=0`

`\log_33=1`

`\log_3\left((1)/(9)\right)=-2`

`\log_(3)81=4`

Explanation:

`\textsf{Apply log law}: \quad \log_ax=c \iff x=a^c`

Therefore:

`\log_3x=0 \implies x=3^0=1`

`\log_3x=1 \implies x=3^1=3`

`\log_3x=-2\implies x=3^(-2)=(1)/(3^2)=(1)/(9)`

`\log_3x=4 \implies x=3^4=81`

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

`\log_a1=0`

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

`\log_aa=1`

Answer 2

• See below

Explanation:

Let the number is x in each case.

Use the property below:

• logₐc = b ⇒ aᵇ = c or vice versa

We have:

• 
  `log_3x = 0 -->x = 3^0=1 -->log_31=0`
• 
  `log_3x = 1 -->x = 3^1=3 -->log_33=1`
• 
  `log_3x = -2 -->x = 3^(-2)=1/9 -->log_3(1/9)=-2`
• 
  `log_3x = 4 -->x = 3^4=81 -->log_381=4`