Find the Domain y = log of 3x+10-2

Problem

y=(log_)(3*x+10)−2

Solution

1. Identify the restriction for the logarithmic function. The argument of a logarithm must be strictly greater than zero.

2. Set up the inequality for the argument of the log function.

3*x+10>0

3. Isolate the term containing x by subtracting 10 from both sides.

3*x>−10

4. Solve for x by dividing both sides by 3

x>−10/3

5. Express the domain in interval notation. Since x must be greater than −10/3 the interval starts at −10/3 (not included) and goes to infinity.

Final Answer

Domain:(−10/3,∞)

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