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

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Homework Help Overview

The problem involves solving the logarithmic equation LOG3(X+3) + LOG3(X-1) = 1, which falls under the subject area of logarithmic functions and algebra.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to simplify the logarithmic expression and apply the quadratic formula. Some participants question the validity of the roots in relation to the original logarithmic equation, particularly concerning the definition of logarithms for negative values.

Discussion Status

The discussion is ongoing, with participants providing guidance on the importance of considering the domain of the logarithmic function. There is a focus on ensuring that the solutions found are valid within the context of the original equation.

Contextual Notes

Participants note that logarithms are not defined for negative numbers, which is a critical constraint in determining valid solutions for the equation.

Doubell
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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.
 
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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
 
ehild said:
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.
 
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
 

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