Question

ln(1/e^x)=lne^3x+4
Solve for the value of x.

Answer 1

Answer:

$\displaystyle \red{{x=-1}}$

Step-by-step explanation:

Given :

$\displaystyle{\ln\left(\frac{1}{e^x}\right) =\ln e^{3x+4}}$

On comparing both side we get :

$\displaystyle{\left(\frac{1}{e^x}\right) = e^{3x+4}}\\\\\\\displaystyle{\left(\frac{1}{e^x}\right) = e^{3x}.e^4}\\\\\\\displaystyle{\left(\frac{1}{e^x}\right) = (e^{x})^3.e^4}\\\\\\\display \text{Let e^x } = y}\\\\\\\displaystyle{\left(\frac{1}{y}\right) = y^{3}.e^4}\\\\\\\displaystyle{\left(\frac{1}{e^4}\right) = y^4}$

$\displaystyle{\left(\frac{1}{e}\right)^4 = y^4}\\\\\\\displaystyle{y =\frac{1}{e}}\\\\\\\displaystyle{e^x=\frac{1}{e}}\\\\\\\displaystyle{e^x=e^{-1}}\\\\\\\displaystyle{\rightarrow x=-1}$

Hence we get answer.