Solve the logarithmic equation.

Question

Solve the logarithmic equation.

 

log x + log 2x = 2

 

the solution is x = ?

 

(type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed)

Answer 1

 Log X + Log 2X = 2                / Use identity : Log ( A.B ) = Log A + Log B

 

   Log ( X . 2X) = log 10²

 

 

    2 X^2 = 100

 

     X^2 = 50

 

       X = ±√50  ,   +√50 is the only acceptable.

 

      Test

 

      log ( √50 * 2 √50 ) = log ( 2* 50) = log 100 =2

             Check