Find the Domain log base 3 of 5x+2- log base 3 of x-2=2

Problem

(log_3)(5*x+2)−(log_3)(x−2)=2

Solution

1. Identify the arguments of the logarithmic functions in the equation.

2. Set the argument of the first logarithm to be strictly greater than zero, as the domain of (log_b)(u) is u>0

5*x+2>0

3. Solve the first inequality for x

5*x>−2

x>−2/5

4. Set the argument of the second logarithm to be strictly greater than zero.

x−2>0

5. Solve the second inequality for x

x>2

6. Determine the intersection of the two conditions x>−2/5 and x>2 to find the values of x for which the entire expression is defined.

x>2

Final Answer

Domain:(2,∞)

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