SOLUTION: Solve the equation log 3√x^2+1 = 1/3. log (cube root x^2+1)=1/3

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve the equation log 3√x^2+1 = 1/3. log (cube root x^2+1)=1/3      Log On


   

Question 1162018: Solve the equation log 3√x^2+1 = 1/3.
log (cube root x^2+1)=1/3
Answer by ikleyn(52831) About Me  (Show Source):
You can put this solution on YOUR website!
.

Your original equation is


    log%28root%283%2Cx%5E2%2B1%29%29 = 1%2F3.


It means that


    root%283%2Cx%5E2%2B1%29 = 10^(1/3).


Cube both sides.  You will get then


    x%5E2+%2B+1 = 10,


which implies


    x^2 = 10 - 1 = 9


    x = +/- sqrt%289%29 = +/- 3.


ANSWER.  The given equation has 2 (two) solutions:  x= 3  and  x= -3.


You can  CHECK  it on your own that both values satisfy the original equation.
For it, simply substitute the values into the equation.

Solved.