= Solution
The passive <RC low-pass filter> is simple, inexpensive, requires no power supply, and has no <operational amplifier> saturation or finite <bandwidth> limitation. It offers no <voltage gain>; its <output impedance> is finite, and both source <electrical resistance> and loading can change the observed <frequency response>. Its <resistor> also produces <thermal noise>.
The active <inverting low-pass amplifier> provides a low-<frequency> <voltage gain> of magnitude five and, within the usable <bandwidth>, a small <output impedance>, so it can drive a load with much less change in <frequency response>. The input <electrical resistance> is approximately $R_1=1\,\mathrm{k}\Omega$ and may itself load the source. It needs a power supply and adds <electrical noise> and offset; finite <operational amplifier> gain, <bandwidth>, <slew rate>, available output swing, and output <electric current> limit the ideal formula. Its inversion must also suit the application. The best choice depends on required <voltage gain>, source and load <electrical impedances>, and the signal's <frequency> and <amplitude>.
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