Question

What is the logarithmic form of the equation e5x ≈ 4768?

log5x4768 = e
5 logxe = 4768
ln 4768 = 5x
ln 5x = 4768

Answer 1

ln 4768 = 5x is the logarithmic form of the equation
`e^(5x)` = 4768.

Explanation:

Given :
`e^(5x)` = 4768.

To find : What is the logarithmic form of the equation .

Solution : We have given that
`e^(5x)` = 4768.

By logarithm properties :

`(i)~\ln a^b=b\ln a,\\\\(ii)~\ln e=1.`.

Taking logarithm both side

`ln\ e^(5x) = ln 4768`

By property (1)

`5x\ ln e = ln\ 4768`.

BY property (2)

5x × 1 = ln4768

5x = ln4768.

Therefore, ln 4768 = 5x is the logarithmic form of the equation
`e^(5x)` = 4768.

Answer 2

Answer: The answer is (c) ln 4768 = 5x.

Step-by-step explanation: The given equation is

`e^(5x)=4768.`

We are to find the logarithmic form of the above equation.

We will be using the following properties of logarithm :

`(i)~\ln a^b=b\ln a,\\\\(ii)~\ln e=1.`

The solution is as follows:

`e^(5x)=4768\\\\\Rightarrow \ln{e^(5x)}=\ln 4768\\\\\Rightarrow 5x\ln e=\ln 4768\\\\\Rightarrow 5x* 1=\ln4768\\\\\Rightarrow 5x=4768.`

Thus, the correct option is (c).