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I am having trouble getting the right answer to the question.Any help would be appreciated: $$ 4\cdot 3^{2x} =\mathrm{e}^x. $$

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    Take the log of both sides? – 2017-02-21
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    yes this is the equation – 2017-02-21

1 Answers 1

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Taking the $\log$ of both sides, you get

$$\log(4\cdot 3^{2x})=\log(e^x),$$

and using the properties of the logarithm, you get:

$$\log(4)+2x\log(3)=x$$

and it is now a simple linear equation for you to solve.

The final result is:

$$x=\frac{\log 4}{1-2\log 3}.$$

The properties of the logarithm I used are:

  • $\log(ab)=\log a+\log b$,

  • $\log(a^q)=q\log a$,

  • $\log(e^x)=x$.

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    @MuskanPirzada I am glad I could helped, you can accept the answer if it suits you. – 2017-02-21