Find the Domain log of x+2 = log of 3x-3

Problem

(log_)(x+2)=(log_)(3*x−3)

Solution

1. Identify the constraints for the logarithmic functions, as the argument of a logarithm must be strictly greater than zero.

2. Set up the inequality for the first term:

x+2>0

3. Solve for x in the first inequality:

x>−2

4. Set up the inequality for the second term:

3*x−3>0

5. Solve for x in the second inequality:

3*x>3

x>1

6. Determine the intersection of the two conditions x>−2 and x>1 to find the values of x for which both logarithms are defined.

7. Conclude that since 1>−2 the intersection is x>1

Final Answer

Domain:x>1

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