Verified Answer :

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:

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

Thus, the correct option is (c).

Answer:

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

Step-by-step 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.

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