Question

Logarithmic Form Express the equation in logarithmic form.

(a)$e^x=2$ (b)$e^3=y$

Short answer

1. Logarithmic form of $e^x=2$is $\ln \left(2\right)=x$.
2. Logarithmic form of $e^3=y$is $\ln \left(y\right)=3$.

Step-by-step solution

Part a. Step 1. Given.

The given exponential form is $e^x=2$.

Part a. Step 2. To determine.

We have to find the exponential form.

Part a. Step 3. Calculation.

We’ll use the formula:$e^b=c$ is equivalent to $\ln c=b$.

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

Exponential form ($e^b=c$)	b	c	Logarithmic form ($\ln c=b$)
$e^x=2$	x	2	$\ln \left(2\right)=x$

Hence, logarithmic form of $e^x=2$is $\ln \left(2\right)=x$.

Part b. Step 1. Given.

The given exponential form is $e^3=y$.

Part b. Step 2. To determine.

We have to find the exponential form.

Part b. Step 3. Calculation.

We’ll use the formula:$e^b=c$ is equivalent to $\ln c=b$.

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

Exponential form ($e^b=c$)	b	c	Logarithmic form ($\ln c=b$)
role="math" localid="1648553747062" $e^3=y$	3	y	$\ln \left(y\right)=3$

Hence, logarithmic form of $e^3=y$is $\ln \left(y\right)=3$.