If the cost of a competing factor of production, such as a machine that also could do the job, rises. This would result in a shift in the demand for this factor out to the right and would put pressure on the wage to rise. I don't understand why this is the case because I thought if machines replaced human labor then wouldn't wages be lower because there wouldn't be a need for human labor?

Keep in mind that we're framing it based on what the first sentence says, which is "If the cost of a competing factor of production, such as a machine that also could do the job, rises".

So if the cost of getting a machine part, various parts, or the entire machine cost rises, then demand for the machine will go down. This will make employers seek out substitutes. In this case, those substitutes would be human labor. As employers demand for labor goes up, the wages will rise assuming the supply of workers is held constant. If the supply of workers increased, then you could argue the wages could go down. So that's why I'm assuming the supply is held in check.

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