Natural Logs

ln(x) + ln(4x)  =  2

          ln(4x²)  =  2                                 (adding logs  --->  multiplying numbers)

                4x²  =  e²                               (raise both sides to the power of e)

                  x²  =  e² / 4                           

                    x  =  e/2

I may be wrong.

 

ln(x) + ln(4x) = 2

 

First, raise each side by e.

 

 ln(x) +  ln(4x) =   2

e         e            e

 

Afterwards, simplify.

                     2

(x) + (4x) = e

 

           2

5x  = e

 

More simplification, (Divide by 5)

          2

x =   e

      -----

        5

                  2

Compute e    = 7.389

 

x =  7.389

       -----

        5

 

Finalize answer.

 

x = 1.477

Good try guest answerer but

 

ln(x) + ln(4x) = 2

 

\(ln(x) + ln(4x) = 2\\ e^{ln(x) + ln(4x) }=e^ 2\\ e^{ln(x) } \textcolor{red}{\times }e^{ ln(4x) }=e^ 2\\ x \textcolor{red}{\times }4x=e^ 2\\ 4x^2=e^ 2\\ etc\)