Questions: Find the domain of y=log(5+2x).

Find the domain of y=log(5+2x).
Transcript text: Find the domain of $y=\log (5+2 x)$.
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Solution

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Solution Steps

Step 1: Identify the Argument of the Logarithm

The argument of the logarithm is given by \(b + mx\). In this case, it is \( 5 + 2x\).

Step 2: Set the Argument Greater Than Zero

For the logarithm to be defined, its argument must be greater than zero. Therefore, we set \( 5 + 2x > 0\).

Step 3: Solve the Inequality for \(x\)

Since \(m > 0\), the solution to the inequality \( 5 + 2x > 0\) is \(x > -2.5\).

Final Answer: The domain of \(y\) is \(x > -2.5\).

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