Question

Exponential Form Express the equation in exponential form.

(a) ${\log }_{6}z=1$ (b)${\log }_{10}3=2t$

Short answer

1. Exponential form of ${\log }_{6}z=1$is $6^1=z$.
2. Exponential form of ${\log }_{10}3=2t$is ${10}^{2t}=3$.

Step-by-step solution

Part a. Step 1. Given.

The given logarithmic form is ${\log }_{6}z=1$.

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 ($a^b=c$)
${\log }_{6}z=1$	6	1	z	$6^1=z$

Hence, exponential form of ${\log }_{6}z=1$is $6^1=z$.

Part b. Step 1. Given.

The given logarithmic form is ${\log }_{10}3=2t$.

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 ($a^b=c$)
${\log }_{10}3=2t$	10	2t	3	${10}^{2t}=3$

Hence, exponential form of ${\log }_{10}3=2t$is ${10}^{2t}=3$.