How to write the equivalent equation which does not use the log with this problem

Are E and R both just variables or is E really the number e ???

 

If there are 2 variables then you can't solve it with just one equation.

 

However ,if your question to find R given this then..

 

log(e) = 1.2 + 1.81 ln(R)

1= 1.2 + 1.81 ln(R)

-0.2=  1.81 ln(R)

(-0.2/1.81)=  ln(R)

R=e^(-0.2/1.81)

 

e^(-0.2/1.81) = 0.8953888036358034

remember that \(e^{ln(x)}=x\)

Therefore just raise e by each side of the equation to get rid of the log terms

 

Edit:

Also a rule that will help you simplify -> \(e^{a+b}=e^ae^b\)

If you take E and R to be variables:

 

\(\ln{E}=1.2+1.81\ln{R} \\ E = e^{1.2+1.81\ln{R}}\\E = e^{1.2}e^{\ln{R^{1.81}}}\\E=R^{1.81}e^{1.2}\)

 

Which is an equivalent equation without the natural log