Find the Domain log of 10x- log of 2x-3 = log of 8

Problem

(log_)(10*x)−(log_)(2*x−3)=(log_)(8)

Solution

1. Identify the arguments of each logarithmic function in the equation. For a logarithm (log_)(u) to be defined, the argument u must be strictly greater than zero.

2. Set up an inequality for the first logarithmic term, (log_)(10*x)

10*x>0

3. Solve for x in the first inequality by dividing both sides by 10

x>0

4. Set up an inequality for the second logarithmic term, (log_)(2*x−3)

2*x−3>0

5. Solve for x in the second inequality by adding 3 to both sides and then dividing by 2

2*x>3

x>3/2

6. Determine the intersection of the two conditions x>0 and x>3/2 Since 3/2 is greater than 0 the condition x>3/2 satisfies both requirements.

Final Answer

Domain:x>3/2

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