Respuesta :

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

Step-by-step explanation:  The given equation is

[tex]e^{5x}=4768.[/tex]

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

We will be using the following properties of logarithm :

[tex](i)~\ln a^b=b\ln a,\\\\(ii)~\ln e=1.[/tex]

The solution is as follows:

[tex]e^{5x}=4768\\\\\Rightarrow \ln{e^{5x}}=\ln 4768\\\\\Rightarrow 5x\ln e=\ln 4768\\\\\Rightarrow 5x\times 1=\ln4768\\\\\Rightarrow 5x=4768.[/tex]

Thus, the correct option is (c).

Answer:

ln 4768 = 5x is the logarithmic form of the equation [tex]e^{5x}[/tex] = 4768.

Step-by-step explanation:

Given : [tex]e^{5x}[/tex] = 4768.

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

Solution : We have given that  [tex]e^{5x}[/tex] = 4768.

By logarithm  properties :

[tex](i)~\ln a^b=b\ln a,\\\\(ii)~\ln e=1.[/tex].

Taking logarithm both side  

[tex]ln\ e^{5x} = ln 4768[/tex]

By property (1)

[tex]5x\ ln e = ln\ 4768[/tex].

BY property (2)

5x × 1 =  ln4768

5x =  ln4768.

Therefore, ln 4768 = 5x is the logarithmic form of the equation [tex]e^{5x}[/tex] = 4768.

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