Question

Exponential Form Express the equation in exponential form.

(a) ${\log }_{3}81=4$ (b)${\log }_{3}1=0$

Short answer

1. Exponential form of ${\log }_{3}81=4$is $3^4=81$.
2. Exponential form of ${\log }_{3}1=0$is $3^0=1$.

Step-by-step solution

Part a. Step 1. Given.

The given logarithmic form is ${\log }_{3}81=4$.

Part a. Step 2. To determine.

We have to find the exponential form.

Part a. Step 3. Calculation.

We’ll use the formula:$a^b=c$ is equivalent to ${\log }_{a}c=b$.

Comparing we find the values of a, b, c. Then plug them in the exponential form.

Logarithmic form (${\log }_{a}c=b$)	a	b	c	Exponential form ($a^b=c$)
${\log }_{3}81=4$	3	4	81	$3^4=81$

Hence, exponential form of ${\log }_{3}81=4$is $3^4=81$.

Part b. Step 1. Given.

The given logarithmic form is ${\log }_{3}1=0$.

Part b. Step 2. To determine.

We have to find the exponential form.

Part b. Step 3. Calculation.

We’ll use the formula:$a^b=c$ is equivalent to ${\log }_{a}c=b$.

Comparing we find the values of a, b, c. Then plug them in the exponential form.

Logarithmic form (${\log }_{a}c=b$)	a	b	c	Exponential form ($a^b=c$)
${\log }_{3}1=0$	3	0	1	$3^0=1$

Hence, exponential form of ${\log }_{3}1=0$is $3^0=1$.