Solve Logarithm Math Problem: LOG3(X+3)+LOG3(X-1)=1

[Doubell]

Homework Statement

NEED HELP WITH THIS MATH PROBLEM: LOG3(X+3) + LOG3(X-1) = 1

Homework Equations

The Attempt at a Solution

I SAID LOG3(X+3) + LOG3 (X-1)
SIMPLIFIES TO LOG3(X+3)*(X-1) = 1
I.E LOG3(X^2 +2X - 3) = 1
THEN 3^1 = (X^2 +2X - 3)
AND 0 = (X^2 +2X - 6)
THEN USE THE QUADRATIC FORMULA TO FIND X AS {-2+/- 28^1/2}/2
JUST NEED A SECOND OPINION TO SEE IF ITS CORRECT.

 

[ehild]

The calculation is correct so far, but you have to investigate what root is solution of the original equation. Hint: is logarithm defined for negative numbers? ehild

 

[Doubell]

the calculation is correct so far, but you have to investigate what root is solution of the original equation. Hint: Is logarithm defined for negative numbers?


Ehild

ok so logarithms are not defined by negative values hence the root for the original equation would have to be the positive value of x which would have been {-2 +[28^1/2]}/2 is that the final solution.

 

[ehild]

Correct for the real logarithmic function.

(Later you will learn about complex numbers and functions, and the complex logarithm is defined for negative numbers, too. )

ehild